On the binary images of (8, 5) shortened cyclic codes over GF(28)

We consider the binary images of (8, 5) shortened cyclic codes. The (8, 5) shortened cyclic codes have a variety of choices. We have generated about 30000 sample codes with different weight distributions. Let S_w denote the set of generated sample codes with minimum weight w. The largest minimum weight of sample codes is 8. Let A_w denote the number of codewords of weight w of a sample code. In S ₇, the smallest of A₇ is 10 for 10 sample codes and the second smallest of A₇ is 11 for six sample codes. In S₇, the smallest of A₈ is 728 for a sample code and the second smallest of A₈ is 729 for a sample code. We have chosen two sample codes from each of S₇ and S₈ which have the smallest and the second smallest sums of A _w for 7⩽w⩽9 in S₇ and S₈, respectively. For the AWGN channel using BPSK signaling, we have made simulation to evaluate the decoding error probabilities by a soft-decision decoding based on ordered statistics for the chosen four sample codes at SNR 2.0 to 5.0. These error probabilities are considerably smaller than the optimum error probabilities for (64, 40) subcodes of (64, 42) Reed-Muller code