The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
La redondance de séparation est une propriété importante dans l'analyse du décodage d'erreur et d'effacement d'un code de bloc linéaire. Dans ce travail, nous étudions la redondance séparatrice des duaux des codes de Reed-Muller généralisés du premier ordre (GRM), une classe de codes de blocs linéaires non binaires qui ont de belles propriétés algébriques. Le dual d'un code GRM du premier ordre peut être spécifié par deux entiers positifs m et à la q et désigné par R(m,q), où q est la puissance d'un nombre premier et q≠2. Nous déterminons la première valeur de redondance séparatrice de R(m,q) pour toute m et à la q. Nous déterminons également les secondes valeurs de redondance séparatrice de R(m,q) pour toute q et à la m=1 et 2. Pour m≥3, nous posons un problème de programmation linéaire en entier binaire dont l'optimum donne une borne inférieure sur la seconde redondance séparatrice de R(m,q).
Haiyang LIU
the Institute of Microelectronics of Chinese Academy of Sciences
Yan LI
China Agricultural University
Lianrong MA
Tsinghua University
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Haiyang LIU, Yan LI, Lianrong MA, "On the Separating Redundancy of the Duals of First-Order Generalized Reed-Muller Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 1, pp. 310-315, January 2019, doi: 10.1587/transfun.E102.A.310.
Abstract: The separating redundancy is an important property in the analysis of the error-and-erasure decoding of a linear block code. In this work, we investigate the separating redundancy of the duals of first-order generalized Reed-Muller (GRM) codes, a class of nonbinary linear block codes that have nice algebraic properties. The dual of a first-order GRM code can be specified by two positive integers m and q and denoted by R(m,q), where q is the power of a prime number and q≠2. We determine the first separating redundancy value of R(m,q) for any m and q. We also determine the second separating redundancy values of R(m,q) for any q and m=1 and 2. For m≥3, we set up a binary integer linear programming problem, the optimum of which gives a lower bound on the second separating redundancy of R(m,q).
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.310/_p
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@ARTICLE{e102-a_1_310,
author={Haiyang LIU, Yan LI, Lianrong MA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Separating Redundancy of the Duals of First-Order Generalized Reed-Muller Codes},
year={2019},
volume={E102-A},
number={1},
pages={310-315},
abstract={The separating redundancy is an important property in the analysis of the error-and-erasure decoding of a linear block code. In this work, we investigate the separating redundancy of the duals of first-order generalized Reed-Muller (GRM) codes, a class of nonbinary linear block codes that have nice algebraic properties. The dual of a first-order GRM code can be specified by two positive integers m and q and denoted by R(m,q), where q is the power of a prime number and q≠2. We determine the first separating redundancy value of R(m,q) for any m and q. We also determine the second separating redundancy values of R(m,q) for any q and m=1 and 2. For m≥3, we set up a binary integer linear programming problem, the optimum of which gives a lower bound on the second separating redundancy of R(m,q).},
keywords={},
doi={10.1587/transfun.E102.A.310},
ISSN={1745-1337},
month={January},}
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TY - JOUR
TI - On the Separating Redundancy of the Duals of First-Order Generalized Reed-Muller Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 310
EP - 315
AU - Haiyang LIU
AU - Yan LI
AU - Lianrong MA
PY - 2019
DO - 10.1587/transfun.E102.A.310
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2019
AB - The separating redundancy is an important property in the analysis of the error-and-erasure decoding of a linear block code. In this work, we investigate the separating redundancy of the duals of first-order generalized Reed-Muller (GRM) codes, a class of nonbinary linear block codes that have nice algebraic properties. The dual of a first-order GRM code can be specified by two positive integers m and q and denoted by R(m,q), where q is the power of a prime number and q≠2. We determine the first separating redundancy value of R(m,q) for any m and q. We also determine the second separating redundancy values of R(m,q) for any q and m=1 and 2. For m≥3, we set up a binary integer linear programming problem, the optimum of which gives a lower bound on the second separating redundancy of R(m,q).
ER -