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

Recently Kasami { 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 length2ᵐ - 1withm ≥ 8and designed distance2t + 1with4 ≤ t ≤ 5is improved. From these results, the relative deviation of the number of codewords of weightj≤ 2ᵐ⁻¹from the binomial distribution2⁻ᵐᵗ ( {2ᵐ-1}{j} )is shown to be less than 1 percent for the following cases: (1)t = 4, j ≥ 2t + 1andm ≥ 16; (2)t = 4, j ≥ 2t + 3and10 ≤ m ≤ 15; (3)t=4, j ≥ 2t+5and8 ≤ m ≤ 9; (4)t=5,j ≥ 2t+ 1andm ≥ 20; (5)t=5, j ≥ 2t+ 3and12 ≤ m ≤ 19; (6)t=5, j ≥ 2t+ 5and10 ≤ m ≤ 11; (7)t=5, j ≥ 2t + 7andm=9; (8)t= 5, j ≥ 2t+ 9andm = 8.