On the Separating Redundancy of the Duals of First-Order Generalized Reed-Muller Codes

Haiyang LIU  Yan LI  Lianrong MA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A    No.1    pp.310-315
Publication Date: 2019/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.310
Type of Manuscript: LETTER
Category: Coding Theory
separating redundancy,  separating matrix,  generalized Reed-Muller (GRM) codes,  duals,  binary integer linear programming,  

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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).