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

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4 Author(s)

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 .

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IEEE Transactions on Information Theory  (Volume:32 ,  Issue: 5 )