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coding THEORY ON h(x) fibonacci p-NUMBERS POLYNOMIALS

DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS 2012年第3期4卷 1250030页

作者： Basu, Manjusri Prasad, Bandhu Univ Kalyani Dept Math Kalyani 741235 W Bengal India Kandi Raj Coll Dept Math Kandi 742137 India

In this paper, we introduce h(x) fibonacci p-numbers polynomials and a new fibonacci Q(p,h)(x) matrix for h(x) fibonacci p-numbers polynomials where p(> 0) is integer and h(x)(> 0) is a polynomial with real coefficients. Thereby, we discuss various properties of Q(p,h)(x) matrix and the coding theory followed from the Q(p,h)(x) matrix. We establish the relations among the code matrix elements for p(> 0) is integer and h(x)(> 0). We also show that the relations, among the code matrix elements for h(x) = m(> 0), coincide with the relations among the code matrix elements for coding theory on the m-extension of the fibonacci p-numbers. The relations among the code matrix elements for h(x) = 1, coincide with the generalized relations among the code matrix elements for fibonacci coding theory. In general, correct ability of this method, which is independent of h(x), increases as p increases but h(x) being a polynomial, improves the cryptography protection.

关键词： fibonacci numbers fibonacci p-numbers fibonacci matrix fibonacci coding code matrix m-extension of the fibonacci p-numbers correct ability

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A new class of fibonacci sequence based error correcting codes

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2017年第3期9卷 379-396页

作者： Esmaeili, M. Moosavi, M. Gulliver, T. A. Isfahan Univ Technol Dept Math Sci Esfahan *** Iran Univ Victoria Dept Elect & Comp Engn POB 1700 Victoria BC V8W 2Y2 Canada

A new class of matrices is introduced for use in error control coding. This extends previous results on the class of fibonacci error correcting codes. For a given integer p, a (p + 1) x (p + 1) binary matrix M-p is given whose nonzero entries are located either on the superdiagonal or the last row of the matrix. The matrices M-p(n) and M-p(-n), the nth power of M-p and its inverse, are employed as the encoding and decoding matrices, respectively. It is shown that for sufficiently large n, independent of the message matrix M, relations exist among the elements of the encoded matrix E = M x M-p(n). These relations play a key role in the error detection and correction.

关键词： fibonacci coding Encoding matrix fibonacci sequence

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fibonacci Codes for Crosstalk Avoidance

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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 2012年第10期20卷 1899-1903页

作者： Mutyam, Madhu Indian Inst Technol Dept Comp Sci & Engn Madras 600036 Tamil Nadu India

Propagation delay across long on-chip buses is significant when adjacent wires are transitioning in opposite direction (i.e., crosstalk transitions) as compared to transitioning in the same direction. By exploiting fibonacci number system, we propose a family of fibonacci coding techniques for crosstalk avoidance, relate them to some of the existing crosstalk avoidance techniques, and show how the encoding logic of one technique can be modified to generate codewords of the other technique.

关键词： On-chip bus crosstalk fibonacci coding

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Long range variations on the fibonacci universal code

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JOURNAL OF NUMBER THEORY 2010年第9期130卷 1925-1931页

作者： Basu, Manjusri Prasad, Bandhu Univ Kalyani Dept Math Kalyani 741235 W Bengal India

fibonacci coding is based on fibonacci numbers and was defined by Apostolico and Fraenkel (1987) [1]. fibonacci numbers are generated by the recurrence relation F(i) = F(i-1) + F(i-2) for all i >= 2 with initial terms F(0) = 1, F(1) = 1. Variations on the fibonacci coding are used in source coding as well as in cryptography. In this paper, we have extended the table given by Thomas In We have found that there is no Gopala-Hemachandra code for a particular positive integer n and for a particular value of a a is an element of Z. We conclude that for n = 1, 2.3, 4, Gopala-Hemachandra code exists for a = -2, -3 ..... -20. Also, for 1 <= n <= 100, there is at most m consecutive not available (N/A) Gopala-Hemachandra code in GH(-(4+m)) column where 1 <= in <= 16. And, for 1 <= n <= 100, as in increases the availability of Gopala-Hemachandra code decreases in GH-(4+m) column where 1 <= m <= 16. C) 2010 Elsevier Inc. All rights reserved.

关键词： fibonacci numbers fibonacci coding Zeckendorf's representation Gopala-Hemachandra sequence and codes Elias code

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The generalized k-sequence

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JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY 2019年第6期22卷 943-952页

作者： Kuhapatanakul, Kantaphon Laohakosol, Vichian Kasetsart Univ Dept Math Bangkok 10900 Thailand

A new notion, called generalized k-sequence, which is a sequence satisfying a second order linear recurrence with coefficients depending on two independent parameters, is introduced. The set of such sequences contains almost all previously known extensions of the fibonacci and Lucas sequences. Properties of the generalized k-sequence are derived, and a new coding-decoding method arising from such sequences is developed.

关键词： k-sequence fibonacci numbers Lucas numbers fibonacci coding code matrix

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TRIBONACCI MATRICES AND A NEW coding THEORY

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DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS 2014年第1期6卷 1450008-1-1450008-17页

作者： Basu, Manjusri Das, Monojit Univ Kalyani Dept Math Kalyani 741235 W Bengal India

In this paper, we consider the series of Tribonacci numbers. Thereby, we introduce a new coding theory called Tribonacci coding theory based on Tribonacci numbers and show that in the simplest case, the correct abilit... 详细信息

关键词： fibonacci numbers Tribonacci numbers fibonacci matrices Tribonacci matrices fibonacci coding Tribonacci coding

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Crosstalk Free coding Systems to Protect NoC Channels Against Crosstalk Faults 35

Crosstalk Free Coding Systems to Protect NoC Channels Agains...

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35th IEEE International Conference on Computer Design (ICCD)

作者： Soleimani, Kimia Patooghy, Ahmad Soltani, Nasim Bu, Lake Kinsy, Michel A. Boston Univ Dept Elect & Comp Engn Adapt & Secure Comp Syst ASCS Lab Boston MA 02215 USA

ISBN: (纸本)9781538622544

Reliability of modern multicore and many-core chips is tightly coupled with the reliability of their on-chip networks. Communication channels in current Network-on-Chips (NoCs) are extremely susceptible to crosstalk faults. In this work, we propose a set of rules for generating classes of crosstalk free coding systems to protect communication channels in NoCs against crosstalk faults. Codewords generated through these rules are free of '101' and '010' bit patterns, which are the main sources of crosstalk faults in NoC communication channels. The proposed rules determine: (1) the weights of different bit positions in a coding system to reach crosstalk free codings, and (2) how the coding might be utilized in an NoC to prevent crosstalk generating bit patterns in NoC channels. Using the proposed set of rules, designers can obtain coding systems which are crosstalk free for any widths of communication channels. Compared to conventional Forbidden Pattern Free (FPF) systems, the proposed methodology is able to provide unique representation to any input values at the lower bound of the codeword lengths. Analyses show that the proposed rules, along with the proposed encoding/decoding mechanisms, are effective in preventing forbidden pattern coding systems for network-on-chips of any arbitrary channel width.

关键词： Crosstalk Fault Network on Chips fibonacci coding Crosstalk Free coding Forbidden Pattern Free

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