Information Sets From Defining Sets for Reed-Muller Codes of First and Second Order

被引：2

作者：

Joaquin Bernal, Jose ^{[1
]}

Simon Pinero, Juan Jacobo ^{[1
]}

机构：

[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2018年 / 64卷 / 10期

关键词：

Abelian codes; Reed-Muller codes; information sets; defining sets;

D O I：

10.1109/TIT.2018.2817539

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Reed-Muller codes belong to the family of affine-invariant codes. As such codes, they have a defining set that determines them uniquely, and they are extensions of cyclic group codes. In this paper, we identify those cyclic codes with multidimensional abelian codes and we use the techniques introduced by Bernal and Simon to construct information sets for them from their defining set. For first- and second-order Reed-Muller codes, we describe a direct method to construct information sets in terms of their basic parameters.

引用

页码：6484 / 6497

页数：14

共 18 条

[11] Reed-Muller Codes: Information Sets from Defining Sets
Joaquin Bernal, Jose
Jacobo Simon, Juan
[J]. CODING THEORY AND APPLICATIONS, ICMCTA 2017, 2017, 10495 : 30 - 47
[12] Partial Permutation Decoding for Abelian Codes
Joaquin Bernal, Jose
Jacobo Simon, Juan
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2013, 59 (08) : 5152 - 5170
[13] Information Sets From Defining Sets in Abelian Codes
Joaquin Bernal, Jose
Jacobo Simon, Juan
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (12) : 7990 - 7999
[14] Information sets and partial permutation decoding for codes from finite geometries
Key, JD
McDonough, TP
Mavron, VC
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2006, 12 (02) : 232 - 247
[15] Partial permutation decoding for codes from finite planes
Key, JD
McDonough, TP
Mavron, VC
[J]. EUROPEAN JOURNAL OF COMBINATORICS, 2005, 26 (05) : 665 - 682
[16] Muller D. E., 1954, Transactions of the IRE professional group on electronic computers, V3, P6, DOI 10.1109/IREPGELC.1954.6499441
[17] A CLASS OF MULTIPLE-ERROR-CORRECTING CODES AND THE DECODING SCHEME
REED, IS
[J]. IRE TRANSACTIONS ON INFORMATION THEORY, 1954, (04): : 38 - 49
[18] Partial permutation decoding for the first-order Reed-Muller codes
Seneviratne, P.
[J]. DISCRETE MATHEMATICS, 2009, 309 (08) : 1967 - 1970

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