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EVERY BAD CODE HAS A GOOD subcode - LOCAL CONVERSE TO CODING THEOREM

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE 1976年第2期34卷 179-182页

作者： AHLSWEDE, R DUECK, G UNIV BIELEFELD MATH FAK KURT SCHUMACHER STR 6 D-4800 BIELEFELD GERMANY

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Relations between the local weight distributions of a linear block code, its extended code, and its even weight subcode

Relations between the local weight distributions of a linear...

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IEEE International Symposium on Information Theory

作者： Yasunaga, K Fujiwara, T Osaka Univ Grad Sch Informat Sci & Technol Suita Osaka 5650871 Japan

ISBN: (纸本)0780391500

Relations between the local weight distributions of a binary linear code, its extended code, and its even weight subcode are presented. In particular, for a code of which the extended code is transitive invariant and contains only codewords with weight multiples of four, the local weight distribution can be obtained from that of the extended code. Using the relations, the local weight distributions of the (127, k) primitive BCH codes for k <= 50, the (127, 64) punctured third-order Reed-Muller, and their even weight subcodes are obtained from the local weight distribution of the (128, k) extended primitive BCH codes for k <= 50 and the (128,64) third-order Reed-Muller code. We also show an approach to improve an algorithm for computing the local weight distribution proposed before.

关键词： BCH codes Reed-Muller codes binary codes block codes linear codes (127, 64) punctured third-order Reed-Muller (127, k) extended primitive BCH codes (128, 64) third-order Reed-Muller code binary linear code even weight subcode extended code linear block c linear codes extended code BCH codes Reed-Muller codes binary code Block codes subcode linear block

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An analysis on equal width quantization and linearly separable subcode encoding-based discretization and its performance resemblances

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EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING 2011年第1期2011卷 1-14页

作者： Lim, Meng-Hui Teoh, Andrew Beng Jin Toh, Kar-Ann Yonsei Univ Sch Elect & Elect Engn Coll Engn Seoul 120749 South Korea

Biometric discretization extracts a binary string from a set of real-valued features per user. This representative string can be used as a cryptographic key in many security applications upon error correction. Discretization performance should not degrade from the actual continuous features-based classification performance significantly. However, numerous discretization approaches based on ineffective encoding schemes have been put forward. Therefore, the correlation between such discretization and classification has never been made clear. In this article, we aim to bridge the gap between continuous and Hamming domains, and provide a revelation upon how discretization based on equal-width quantization and linearly separable subcode encoding could affect the classification performance in the Hamming domain. We further illustrate how such discretization can be applied in order to obtain a highly resembled classification performance under the general Lp distance and the inner product metrics. Finally, empirical studies conducted on two benchmark face datasets vindicate our analysis results.

关键词： subcode Quantization Discretization binary string Separable secret key

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QUASI-CYCLIC subcodeS OF CYCLIC CODES

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SIAM JOURNAL ON DISCRETE MATHEMATICS 2017年第2期31卷 1454-1475页

作者： Belfiore, Jean-Claude Guneri, Cem Ozkaya, Buket Telecom ParisTech Dept Comelec 46 Rue Barrault F-75634 Paris 13 France Sabanci Univ Fac Engn & Nat Sci TR-34956 Istanbul Turkey

We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent to enumeration of certain vector subspaces in finite fields. In particular, we present enumeration results for quasi-cyclic subcodes of the simplex code and duals of certain Bose-Chaudhuri-Hocquenqhem codes. Our results are based on the trace representation of cyclic codes.

关键词： cyclic code quasi-cyclic code subcode index enumeration

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On the number of minimum weight codewords of subcodes of Reed-Muller codes

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1998年第10期E81A卷 1990-1997页

作者： Tokushige, H Takata, T Kasami, T Nara Inst Sci & Technol Grad Sch Informat Sci Ikoma 6300101 Japan Iwate Prefectural Univ Fac Software & Informat Sci Morioka Iwate 0200173 Japan Hiroshima City Univ Dept Comp Sci Fac Informat Sci Hiroshima 7313194 Japan

In this paper, we consider linear subcodes of RMr, m whose bases are formed from the monomial basis of RMr, (m) by deleting Delta K monomials of degree r where Delta K < ((m)(r)). For such subcodes, a procedure for computing the number ber of minimum weight codewords is presented and it is shown how to delete Delta K monomials in order to obtain a subcode with the smallest number of codewords of the minimum weight. For Delta K less than or equal to 3, a formula for the number of codewords of the minimum weight is presented. A (64, 40) subcode of RM3, 6 is being considered as an inner code in a concatenated coding system for NASA's high-speed satellite communications. For (64,40) subcodes, there are three equivalent classes. For each class, the number of minimum weight codewords, that of the second smallest weight codewords and simulation results on error probabilities of soft-decision maximum likelihood decoding are presented.

关键词： minimum weight codeword Reed-Muller code subcode

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Remark on subcodes of linear complementary dual codes

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INFORMATION PROCESSING LETTERS 2020年 159卷 105963-105963页

作者： Harada, Masaaki Saito, Ken Tohoku Univ Grad Sch Informat Sci Res Ctr Pure & Appl Math Sendai Miyagi 9808579 Japan

We show that any ternary Euclidean (resp. quaternary Hermitian) linear complementary dual [n, k] code contains a Euclidean (resp. Hermitian) linear complementary dual [n, k - 1] subcode for 2 <= k <= n. As a consequence, we derive a bound on the largest minimum weights among ternary Euclidean linear complementary dual codes and quaternary Hermitian linear complementary dual codes. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Linear complementary dual code Minimum weight subcode Combinatorial problems

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Linear subcodes of turbo codes with improved distance spectra

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IEEE TRANSACTIONS ON INFORMATION THEORY 2004年第12期50卷 3291-3294页

作者： Daneshgaran, F Mondin, M Mulassano, P Calif State Univ Los Angeles Dept Elect & Comp Engn Los Angeles CA 90032 USA Politecn Torino Dipartimento Elettron I-10129 Turin Italy

In this correspondence, we present a technique for generation of linear subcodes of a given turbo code with better distance spectrum than the original mother turbo code, via an iterative process of trace-bit injection which minimally reduces code rate, followed by selective puncturing that allows recovery of the rate loss incurred during the trace-bit injection. The technique allows for asymptotic performance improvement of any linear turbo code. In effect, we trim the distance spectrum of a turbo code via elimination of the low distance and/or high multiplicity codewords from the output space of the code. To this end, we perform a greedy minimization of a cost function closely related to the asymptotic bit error probability (or frame error probability) of the code. This improves the performance of the code everywhere, but its main impact is a reduction in the error floor of the turbo code which is important for delay constrained applications employing short interleavers.

关键词： code doping delay constrained turbo codes distance spectrum interleavers optimization puncturing short length turbo codes subcode trace-bit injection turbo codes

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ON THE COVERING RADIUS OF subcodeS OF A CODE

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IEEE TRANSACTIONS ON INFORMATION THEORY 1991年第6期37卷 1706-1707页

作者： HOU, XD Department of Mathematics and Statistics Wright State University Dayton OH USA

Let C be a binary linear code with covering radius R, and C0 a subcode of C of codimension i. An upper bound is obtained for the covering radius of C0 in terms of R and i. When C0 = {0}, the bound becomes the sphere c... 详细信息

关键词： COVERING RADIUS subcode CHROMATIC NUMBER

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On the symmetry group of the Mollard code

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PROBLEMS OF INFORMATION TRANSMISSION 2016年第3期52卷 265-275页

作者： Mogilnykh, I. Yu. Solov'eva, F. I. Russian Acad Sci Sobolev Inst Math Siberian Branch Novosibirsk Russia

We study the symmetry group of a binary perfect Mollard code M(C,D) of length tm + t + m containing as its subcodes the codes C (1) and D (2) formed from perfect codes C and D of lengths t and m, respectively, by adding an appropriate number of zeros. For the Mollard codes, we generalize the result obtained in [1] for the symmetry group of Vasil'ev codes;namely, we describe the stabilizer Sym(M(C,D)) of the subcode D (2) in the symmetry group of the code M(C,D) (with the trivial function). Thus we obtain a new lower bound on the order of the symmetry group of the Mollard code. A similar result is established for the automorphism group of Steiner triple systems obtained by the Mollard construction but not necessarily associated with perfect codes. To obtain this result, we essentially use the notions of "linearity" of coordinate positions (points) of a nonlinear perfect code and a nonprojective Steiner triple system.

关键词： Magnetic circular dichroism ideal coding Codes Symmetry subcode SYMMETRY GROUPS Perfect

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On bit-error probability of a concatenated coding scheme

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IEEE TRANSACTIONS ON COMMUNICATIONS 1997年第5期45卷 536-543页

作者： Kasami, T Takata, T Yamashita, K Fujiwara, T Lin, S OSAKA UNIV FAC ENGN SCI TOYONAKA OSAKA 560 JAPAN UNIV HAWAII MANOA DEPT ELECT ENGN HONOLULU HI 96822 USA

This paper presents a method for evaluating the bit-error probability of a concatenated coding system for BPSK transmission over the AWGN channel, In the concatenated system, a linear Binary block code is used as the inner code and is decoded with the soft-decision maximum likelihood decoding, and a maximum distance separable code (or its interleaved code) is used as the outer code and is decoded with a bounded distance decoding, The method is illustrated through a specific example in which the inner code is a binary (64,40,8) Reed-Muller subcode and the outer code is the NASA standard (255,223,33) Reed-Solomon code over GF(2(8)) interleaved to a depth of 5, This specific concatenated system is being considered for NASA's high-speed satellite communications, The bit-error performance is evaluated by a combination of simulation and analysis, The split weight enumerators for the maximum distance separable codes are derived and used for the analysis.

关键词： .outer code Coding Scheme inner code soft-decision block code subcode evaluating the bit-error concatenated coding system bit-error performance

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