On the binary images of (8, 5) shortened cyclic codes over GF(2/sup 8/)
Hitoshi Tokushige, T. Tanoue, Tadao Kasami · 2002
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/sub w/ denote the set of generated sample codes with minimum weight w. The largest minimum weight of sample codes is 8. Let A/sub w/ denote the number of codewords of weight w of a sample code. In S/sub 7/, the smallest of A/sub 7/ is 10 for 10 sample codes and the second smallest of A/sub 7/ is 11 for six sample codes. In S/sub 7/, the smallest of A/sub 8/ is 728 for a sample code and the second smallest of A/sub 8/ is 729 for a sample code. We have chosen two sample codes from each of S/sub 7/ and S/sub 8/ which have the smallest and the second smallest sums of A/sub w/ for 7/spl les/w/spl les/9 in S/sub 7/ and S/sub 8/, 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.