مرکز منطقه ای اطلاع رساني علوم و فناوري - An approximation to the weight distribution of binary primitive BCH codes with designed distances 9 and 11 (Corresp.)

DocumentCode :

941985

Title :

An approximation to the weight distribution of binary primitive BCH codes with designed distances 9 and 11 (Corresp.)

Author :

Fujiwara, Tohru ; Takata, Toyoo ; Kasami, Tadao ; Lin, Shu

Volume :

Issue :

fYear :

1986

fDate :

9/1/1986 12:00:00 AM

Firstpage :

706

Lastpage :

709

Abstract :

Recently Kasami {em et al.} presented a linear programming approach to the weight distribution of binary linear codes [2]. Their approach to compute upper and lower bounds on the weight distribution of binary primitive BCH codes of length $2^{m} - 1$ with $m \\geq 8$ and designed distance $2t + 1$ with $4 \\leq t \\leq 5$ is improved. From these results, the relative deviation of the number of codewords of weight $j\\leq 2^{m-1}$ from the binomial distribution $2^{-mt} \\left( stackrel{2^{m}-1}{j} \\right)$ is shown to be less than 1 percent for the following cases: (1) $t = 4, j \\geq 2t + 1$ and $m \\geq 16$ ; (2) $t = 4, j \\geq 2t + 3$ and $10 \\leq m \\leq 15$ ; (3) $t=4, j \\geq 2t+5$ and $8 \\leq m \\leq 9$ ; (4) $t=5,j \\geq 2t+ 1$ and $m \\geq 20$ ; (5) $t=5, j \\geq 2t+ 3$ and $12 \\leq m \\leq 19$ ; (6) $t=5, j \\geq 2t+ 5$ and $10 \\leq m \\leq 11$ ; (7) $t=5, j \\geq 2t + 7$ and $m=9$ ; (8) $t= 5, j \\geq 2t+ 9$ and $m = 8$ .