Upper Bound on the Bit Error Probability of Systematic Binary Linear Codes via Their Weight Spectra

Table 1

The partial IOWEF {, , } with of the BCH code [127, 106].

1	7	17	3	19	1847	5	20	2627123	7	15	2.364896e + 009
1	8	8	3	20	584	5	21	984117	7	16	3.415877e + 009
1	9	2	3	21	127	5	22	288687	7	17	4.098554e + 009
1	10	4	3	22	21	5	23	64158	7	18	4.098554e + 009
1	11	23	4	7	3470	5	24	10105	7	19	3.415535e + 009
1	12	27	4	8	15952	5	25	1049	7	20	2.364660e + 009
1	13	13	4	9	46995	5	26	59	7	21	1351255504
1	14	3	4	10	125279	6	7	19462	7	22	630548101
1	15	8	4	11	275791	6	8	194386	7	23	236462455
1	16	1	4	12	484126	6	9	1059704	7	24	69546072
2	7	71	4	13	697948	6	10	4752113	7	25	15457425
2	8	188	4	14	834510	6	11	16623036	7	26	2439979
2	9	305	4	15	834260	6	12	44331232	7	27	243848
2	10	472	4	16	696623	6	13	94527372	7	28	11614
2	11	711	4	17	482965	6	14	165420289	8	8	163532
2	12	1007	4	18	275130	6	15	239125721	8	9	2946230
2	13	964	4	19	128772	6	16	286915986	8	10	29469636
2	14	794	4	20	47734	6	17	286915986	8	11	192045523
2	15	511	4	21	14385	6	18	239077900	8	12	864339336
2	16	340	4	22	3172	6	19	165519571	8	13	2.924072e + 009
2	17	135	4	23	513	6	20	94593564	8	14	7.797383e + 009
2	18	48	4	24	37	6	21	44141017	8	15	1.672354e + 010
2	19	12	4	25	2	6	22	16553366	8	16	2.926719e + 010
2	20	7	5	7	11611	6	23	4864138	8	17	4.226740e + 010
3	7	614	5	8	73116	6	24	1082409	8	18	5.072263e + 010
3	8	2097	5	9	281110	6	25	170775	8	19	5.072258e + 010
3	9	4816	5	10	960971	6	26	17090	8	20	4.226969e + 010
3	10	10482	5	11	2633699	6	27	823	8	21	2.926271e + 010
3	11	18637	5	12	5642851	7	7	13142	8	22	1.672131e + 010
3	12	27236	5	13	9825582	7	8	276537	8	23	7.803514e + 009
3	13	32706	5	14	14197834	7	9	2380926	8	24	2.926377e + 009
3	14	32212	5	15	17043850	7	10	15092372	8	25	860707256
3	15	27027	5	16	17047259	7	11	69866721	8	26	191259366
3	16	18689	5	17	14202094	7	12	237457686	8	27	30195788
3	17	10826	5	18	9829514	7	13	630106871	8	28	3021987
3	18	5000	5	19	5614707	7	14	1350174932	8	29	143670