Generalized hamming weights of q-ary Reed-Muller codes

被引：97
作者：
Heijnen, P [1 ]
Pellikaan, R [1 ]
机构：
[1] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 1998年 / 44卷 / 01期
关键词：
algebraic-geometry codes; generalized Hamming weights; order functions; Reed-Muller codes;
D O I：
10.1109/18.651015
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The order bound on generalized Hamming weights is introduced in a general setting of codes on varieties which comprises both the one point geometric Goppa codes as well as the q-ary Reed-Muller codes. For the latter codes it is shown that this bound is sharp and that they satisfy the double chain condition.
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页码：181 / 196
页数：16
相关论文
共 44 条
[1]  
ASHIKHMIN A, 1994, THESIS MOSCOW
[2]  
BEZRUKOV S, 1996, MINIMAL IDEALS MACAU
[3]  
BOGUSLAVSKY M, IN PRESS FINITE FIEL
[4]  
Buchberger B., 1965, THESIS U INNSBRUCK I
[5]  
Clements G.F., 1969, J COMB THEORY, V7, P230, DOI 10.1016/S0021-9800(69)80016-5
[6]  
COX D, 1992, IDEALS VARIETIES ALG
[7]   ON GENERALIZED REED-MULLER CODES AND THEIR RELATIVES [J].
DELSARTE, P ;
GOETHALS, JM ;
MACWILLI.FJ .
INFORMATION AND CONTROL, 1970, 16 (05) :403-&
[8]   On binary linear codes which satisfy the two-way chain condition [J].
Encheva, SB .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1996, 42 (03) :1038-1047
[9]  
Endler O, 1972, Valuation Theory
[10]   DECODING ALGEBRAIC GEOMETRIC CODES UP TO THE DESIGNED MINIMUM DISTANCE [J].
FENG, GL ;
RAO, TRN .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1993, 39 (01) :37-45
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