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Construction of Optimal Binary Z-Complementary Code Sets with New Lengths Using generalized boolean function

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES boolean functionS AND SEQUENCES 2023年第5期15卷 979-993页

作者： Ghosh, Gobinda Majhi, Sudhan Paul, Subhabrata IIT Patna Math Patna 801103 Bihar India IISc Bangalore Elect Commun Engn CV Raman Rd Bengaluru 560012 Karnataka India

Z-complementary code sets (ZCCSs) are used in multicarrier code-division multiple access (MC-CDMA) systems, for interference-free communication over multiuser and quasiasynchronous environments. In this paper, we propose three new constructions of optimal binary (R2(k+1), 2(k+1), R gamma,gamma )-ZCCS, (R2(k+1), 2(k+1), R2(m2), 2(m2)) -ZCCS and (2(k+1), 2(k+1),3 gamma, 2 gamma)-ZCCS based on generalized boolean functions (GBFs), where gamma = 2(m1-1) + 2(m1-3), m(1) >= 5, k >= 1, m(2) >= 1 and R is any even number. The proposed ZCCSs cover many unreported lengths and a large number of users.

关键词： generalized boolean function Aperiodic correlation Z-complementary code set Complete complementary code

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Some Properties of Correlation function on generalized boolean functions

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Chinese Journal of Electronics 2015年第1期24卷 166-169页

作者： ZHUO Zepeng CHONG Jinfeng WEI Shimin School of Mathematical Science Huaibei Normal University

The relationship among crosscorrelation functions of arbitrary four generalized boolean functions is presented. Based on it, some properties of crosscorrelation function and autocorrelation function are given. The relationship between crosscorrelation function and generalized Walsh-Hadamard transform of functions is characterized. In the process we generalized old results and get new characterizations of cryptographic properties.

关键词： generalized boolean function generalized Walsh-Hadamard transform Crosscorrelation function Autocorrelation function.

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Constructions of Two-Dimensional Golay-ZCZ Array Sets Based on generalized boolean functions

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IEEE SIGNAL PROCESSING LETTERS 2025年 32卷 321-325页

作者： Prakash, Aditya Kao, Tzu-Chieh Majhi, Sudhan Srivastava, Prashant Kumar Chen, Chao-Yu IIT Patna Dept Math Patna 801106 India Natl Cheng Kung Univ Dept Elect Engn Tainan 701401 Taiwan Natl Cheng Kung Univ Inst Comp & Commun Engn Tainan 701401 Taiwan Indian Inst Sci Dept ECE Bangalore 560012 India

Golay sequences with the zero correlation zone (ZCZ), known as Golay-ZCZ sequences, play a pivotal role in reducing intersymbol interference (ISI) during the process of channel estimation in one dimension. Two-dimensional (2-D) Golay complementary array set (GCAS) within their ZCZ has the potential application in multiple input multiple output (MIMO) omnidirectional transmission. In this letter, 2-D Golay-ZCZ array set is constructed by using generalized boolean function (GBF) without utilizing any kernels. The proposed construction provides 2-D Golay-ZCZ array set with various array sizes and large ZCZ sizes. Also, we get the one dimensional (1-D) Golay- ZCZ sequence set as a special case of the proposed construction.

关键词： Correlation boolean functions Channel estimation Two-dimensional displays Peak to average power ratio NOMA Array signal processing Zero correlation zone Uplink Time-frequency analysis generalized boolean function Golay-ZCZ array

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generalized boolean functionS AS COMBINERS

GENERALIZED BOOLEAN FUNCTIONS AS COMBINERS

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作者： Oliver Di Nallo NAVAL POSTGRADUATE SCHOOL

学位级别：硕士

In this digital age, cryptography has formed the backbone of many computer functions. Cryptography drives online commerce and allows privileged information safe transit between two parties as well as many other critical internet uses. The presence of a strong pseudo-random number generator (PRNG) is an absolute requirement in modern cryptography. All modern ciphers draw their strength from having this strong generator. There are currently many ways to generate a secure PRNG. Most current PRNGs generate their stream as a sequence of bits. As a result, most tests performed to ensure randomness are made for binary streams. This thesis introduces a way to generate an integer random number stream using generalized boolean functions. Additionally, this thesis discusses how to test an integer stream using binary tests. Data from this thesis suggests that high levels of complexity can be obtained using simple quadratic (or other higher degree) generalized combiners. Additionally, our data discusses the ability to generate sequences with high degrees of randomness using a variety of combiner choices for the generalized boolean function.

关键词： pseudo-random number generator generalized boolean function

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Construction of 16-QAM Complementary Sequences from Non-standard generalized boolean functions 6

Construction of 16-QAM Complementary Sequences from Non-stan...

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6th International Conference on Wireless Communications and Signal Processing (WCSP)

作者： Zeng, Fanxin Qian, Linjie Zhang, Zhenyu Chongqing Commun Inst Chongqing Key Lab Emergency Commun Chongqing 400035 Peoples R China

ISBN: (纸本)9781479973392

The given examples show that the standard 16-QAM Golay-Davis-Jedwab (GDJ) complementary sequences (CSs) cannot be yielded whenever the non-standard generalized boolean functions (GBFs) are fed to Chong, et al's construction. Due to the fact that there exist a large number of the non-standard GBFs available, this paper focuses on the conversion from a non-standard GBF to 16-QAM CSs. By improving Chong, et al's construction, we present a new construction in which one of its inputs is the non-standard GBFs. For a given non-standard GBF, the number of the resultant 16-QAM CSs is determined as well. The proposed sequences can be applied to a CDMA or an OFDM communication system so as to remove multiple access interference (MAI) or to reduce peak-to-mean envelope power ratio (PMEPR), respectively.

关键词： non-standard QPSK GDJ complementary sequences 16-QAM Golay complementary sequences generalized boolean function MAI PMEPR

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A Characterization of generalized boolean functions Employed in CDMA Communications

INTERNATIONAL JOURNAL OF MATHEMATICAL ENGINEERING AND MANAGE...

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INTERNATIONAL JOURNAL OF MATHEMATICAL ENGINEERING AND MANAGEMENT SCIENCES 2024年第2期9卷 352-365页

作者： Singh, Deep Chawla, Anjali Bhogta, Pramod Paul, Amit Cent Univ Punjab Dept Math & Stat Bathinda Punjab India Guru Nanak Dev Univ Dept Math Amritsar Punjab India

In design of secure cryptosystems and CDMA communications, the negabent functions play a significant role. The generalized boolean functions have been extensively studied by Schmidt and established several important results in this setup. In this paper, several characteristics of the generalized nega-Hadamard transform (GNT) of generalized boolean functions like inverse of GNT, generalized nega-cross correlation, generalized nega-Parseval's identity, relationship between GNT and generalized nega-cross correlation have analyzed. We studied the GNT for the derivative of this setup of functions and established the connection of generalized Walsh-Hadamard transform and GNT of derivatives of these functions. Also, the GNT of composition of vectorial boolean function and generalized boolean function is presented. Further, the generalized nega-convolution theorem for generalized boolean function is obtained.

关键词： generalized nega-Hadamard transform (GNT) generalized negabent function generalized nega-cross correlation generalized boolean function

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Partial spread and vectorial generalized bent functions

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DESIGNS CODES AND CRYPTOGRAPHY 2017年第1期85卷 1-13页

作者： Martinsen, Thor Meidl, Wilfried Stanica, Pantelimon Naval Postgrad Sch Monterey Dept Appl Math Monterey CA 93943 USA Austrian Acad Sci Johann Radon Inst Computat & Appl Math Linz Austria

In this paper we generalize the partial spread class and completely describe it for generalized boolean functions from F-2(n) to Z(2)(t). Explicitly, we describe gbent functions from F-2(n) to Z(2)(t), which can be seen as a gbent version of Dillon's PSap class. For the first time, we also introduce the concept of a vectorial gbent function from F-2(n) to Z(q)(m), and determine the maximal value which m can attain for the case q = 2(t). Finally we point to a relation between vectorial gbent functions and relative difference sets.

关键词： generalized boolean function generalized bent function Partial spread Vectorial function Relative difference set

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New z-complementary/complementary sequence sets with non-power-of-two length and low PAPR

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES boolean functionS AND SEQUENCES 2022年第4期14卷 817-832页

作者： Shen, Bingsheng Yang, Yang Fan, Pingzhi Zhou, Zhengchun Southwest Jiaotong Univ Sch Math Chengdu Peoples R China Southwest Jiaotong Univ Key Lab Informat Coding & Transmiss Chengdu Peoples R China

Sequences with low peak-to-average power ratio (PAPR) and desirable lengths are useful and important for orthogonal frequency division multiplexing (OFDM) systems. In this paper, based on the generalized boolean functions (GBFs), a class of q-ary Z-complementary sequence sets (ZCSSs) and a class of complementary sequence sets (CSSs) are constructed. The obtained new ZCSSs and CSSs have low PAPR and non-power-of-two lengths.

关键词： Orthogonal frequency division multiplexing (OFDM) Peak-to-average power ratio (PAPR) Z-complementary sequence set Complementary sequence set generalized boolean function

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A Family of New 16-QAM Golay Complementary Sequences without Higher PEP Upper Bounds

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2020年第2期E103A卷 547-552页

作者： Zeng, Fanxin He, Xiping Xuan, Guixin Zhang, Zhenyu Peng, Yanni Yan, Li Chongqing Technol & Business Univ Chongqing Engn Lab Detect Control & Integrated Sy Chongqing 400067 Peoples R China Chongqing Univ Coll Commun Engn Chongqing 400044 Peoples R China Army Engn Univ PLA Commun NCO Acad Chongqing 400035 Peoples R China

In an OFDM communication system using quadrature amplitude modulation (QAM) signals, peak envelope powers (PEPs) of the transmitted signals can be well controlled by using QAM Golay complementary sequence pairs (CSPs). In this letter, by making use of a new construction, a family of new 16-QAM Golay CSPs of length N = 2(m) (integer m >= 2) with binary inputs is presented, and all the resultant pairs have the PEP upper bound 2N. However, in the existing such pairs from other references their PEP upper bounds can arrive at 3.6N when the worst case happens. In this sense, novel pairs are good candidates for OFDM applications.

关键词： complementary sequence pair 16-QAM constellation generalized boolean function peak envelope power binary signal

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New QAM Complementary Sequences for Control of Peak Envelope Power of OFDM Signals

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IEEE ACCESS 2019年 7卷 89901-89912页

作者： Zeng, Yue Zhang, Lisheng Zeng, Fanxin He, Xiping Xuan, Guixin Zhang, Zhenyu Chongqing Univ Posts & Telecommun Coll Software Engn Chongqing 400065 Peoples R China Chongqing Technol & Business Univ Chongqing Engn Lab Detect Control & Integrated Sy Chongqing 400067 Peoples R China Chongqing Univ Coll Commun Engn Chongqing 400044 Peoples R China PLA Army Engn Univ Commun NCO Acad Chongqing 400035 Peoples R China

By developing new mathematical descriptions of 4(q) (integer q >= 2) quadrature amplitude modulation (QAM) constellation, a novel construction producing 4(q)-QAM complementary sequences (CSs) of length 2(m) (integer m >= 2) is presented. The proposed sequences include the known 4(q)-QAM CSs constructed from Cases I to III constructions, proposed by Li, as special cases. For 16-QAM CSs, the number of the resultant sequences is determined precisely. New sequences have a larger family size so as to increase the code rates. When used in orthogonal frequency-division multiplexing (OFDM) systems, new sequences possess the same peak envelope power (PEP) upper bounds as those of the known sequences referred to above.

关键词： Quadrature amplitude modulation complementary sequences standard Golay-Davis-Jedwab complementary sequences generalized boolean function code rates peak envelope power (PEP)

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