On the weight distribution of second order Reed-Muller codes and their relatives

被引：9
作者：
Li, Shuxing [1 ]
机构：
[1] Otto von Guericke Univ, Fac Math, D-39106 Magdeburg, Germany
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2019年 / 87卷 / 10期
关键词：
Reed-Muller codes; Quadratic forms; Weight distribution;
D O I：
10.1007/s10623-019-00630-z
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The weight distribution of second order q-ary Reed-Muller codes have been determined by Sloane and Berlekamp (IEEE Trans. Inform. Theory, vol. IT-16, 1970) for and by McEliece (JPL Space Progr Summ 3:28-33, 1969) for general prime power q. Unfortunately, there were some mistakes in the computation of the latter one. This paper aims to provide a precise account for the weight distribution of second order q-ary Reed-Muller codes. In addition, the weight distributions of second order q-ary homogeneous Reed-Muller codes and second order q-ary projective Reed-Muller codes are also determined.
引用
收藏
页码：2447 / 2460
页数：14
相关论文
共 11 条
[1]  
[Anonymous], 1983, Encyclopedia Math. Appl.
[2]  
Assmus Jr. E.F., 1992, CAMBRIDGE TRACTS MAT, V103
[3]   Automorphism groups of homogeneous and projective Reed-Muller codes [J].
Berger, TP .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2002, 48 (05) :1035-1045
[4]   THE PARAMETERS OF PROJECTIVE REED-MULLER CODES [J].
LACHAUD, G .
DISCRETE MATHEMATICS, 1990, 81 (02) :217-221
[5]  
LACHAUD G, 1988, LECT NOTES COMPUT SC, V311, P125
[6]   THE MINIMUM DISTANCE OF SOME NARROW-SENSE PRIMITIVE BCH CODES [J].
Li, Shuxing .
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2017, 31 (04) :2530-2569
[7]  
MacWilliams F.J., 1977, N HOLLAND MATH LIB, V16
[8]  
McEliece R. J., 1969, SPACE PROGRAM SUMMAR, V3, P28
[9]   Cyclic subcodes of generalized Reed-Muller codes [J].
Moreno, O ;
Duursma, IM ;
Cherdieu, JP ;
Edouard, A .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (01) :307-311
[10]   WEIGHT ENUMERATOR FOR SECOND-ORDER REED-MULLER CODES [J].
SLOANE, NJA ;
BERLEKAMP, ER .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1970, 16 (06) :745-+
12