IEICE TRANSACTIONS on Fundamentals
On the Separating Redundancy of the Duals of First-Order Generalized Reed-Muller Codes
Summary :
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).
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.1 pp.310-315
- Publication Date
- 2019/01/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.310
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Haiyang LIU
the Institute of Microelectronics of Chinese Academy of Sciences
Yan LI
China Agricultural University
Lianrong MA
Tsinghua University
Keyword
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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},}
Copy
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 -
English
