Information on Result #613949

Linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(5120, 3125, F5, 30) (dual of [3125, 3005, 31]-code) [i]Truncation
2Linear OA(5139, 3148, F5, 31) (dual of [3148, 3009, 32]-code) [i](u, u+v)-Construction
3Linear OA(5142, 3154, F5, 31) (dual of [3154, 3012, 32]-code) [i]
4Linear OA(5127, 3164, F5, 31) (dual of [3164, 3037, 32]-code) [i]VarÅ¡amov–Edel Lengthening
5Linear OA(5128, 3198, F5, 31) (dual of [3198, 3070, 32]-code) [i]
6Linear OA(5129, 3254, F5, 31) (dual of [3254, 3125, 32]-code) [i]
7Linear OA(5130, 3341, F5, 31) (dual of [3341, 3211, 32]-code) [i]
8Linear OA(5131, 3463, F5, 31) (dual of [3463, 3332, 32]-code) [i]
9Linear OA(5132, 3620, F5, 31) (dual of [3620, 3488, 32]-code) [i]
10Linear OA(5133, 3803, F5, 31) (dual of [3803, 3670, 32]-code) [i]
11Linear OA(5134, 4006, F5, 31) (dual of [4006, 3872, 32]-code) [i]
12Linear OA(5135, 4224, F5, 31) (dual of [4224, 4089, 32]-code) [i]
13Linear OA(5136, 3142, F5, 31) (dual of [3142, 3006, 32]-code) [i]✔Construction X with Cyclic Codes
14Linear OA(5132, 3137, F5, 33) (dual of [3137, 3005, 34]-code) [i]✔
15Linear OA(5122, 3137, F5, 29) (dual of [3137, 3015, 30]-code) [i]✔
16Linear OA(5124, 3132, F5, 31) (dual of [3132, 3008, 32]-code) [i]✔
17Linear OA(5125, 3140, F5, 31) (dual of [3140, 3015, 32]-code) [i]✔
18Linear OA(5123, 3132, F5, 30) (dual of [3132, 3009, 31]-code) [i]✔
19Linear OA(5145, 3150, F5, 35) (dual of [3150, 3005, 36]-code) [i]✔
20Linear OA(5128, 3147, F5, 31) (dual of [3147, 3019, 32]-code) [i]✔
21Linear OA(5129, 3150, F5, 31) (dual of [3150, 3021, 32]-code) [i]✔
22Linear OA(5130, 3153, F5, 31) (dual of [3153, 3023, 32]-code) [i]✔
23Linear OA(5131, 3156, F5, 31) (dual of [3156, 3025, 32]-code) [i]✔
24Linear OA(5128, 3152, F5, 30) (dual of [3152, 3024, 31]-code) [i]✔
25Linear OA(5129, 3154, F5, 30) (dual of [3154, 3025, 31]-code) [i]✔
26Linear OA(5125, 3150, F5, 29) (dual of [3150, 3025, 30]-code) [i]✔
27Linear OA(5135, 3170, F5, 31) (dual of [3170, 3035, 32]-code) [i]✔
28Linear OA(5133, 3168, F5, 30) (dual of [3168, 3035, 31]-code) [i]✔
29Linear OA(5131, 3166, F5, 29) (dual of [3166, 3035, 30]-code) [i]✔
30Linear OA(5129, 3164, F5, 28) (dual of [3164, 3035, 29]-code) [i]✔
31Linear OA(5139, 3178, F5, 31) (dual of [3178, 3039, 32]-code) [i]✔
32Linear OA(5141, 3184, F5, 31) (dual of [3184, 3043, 32]-code) [i]✔
33Linear OA(5142, 3187, F5, 31) (dual of [3187, 3045, 32]-code) [i]✔
34Linear OA(5137, 3178, F5, 30) (dual of [3178, 3041, 31]-code) [i]✔
35Linear OA(5139, 3184, F5, 30) (dual of [3184, 3045, 31]-code) [i]✔
36Linear OA(5135, 3178, F5, 29) (dual of [3178, 3043, 30]-code) [i]✔
37Linear OA(5136, 3181, F5, 29) (dual of [3181, 3045, 30]-code) [i]✔
38Linear OA(5128, 3153, F5, 31) (dual of [3153, 3025, 32]-code) [i]✔
39Linear OA(5132, 3159, F5, 31) (dual of [3159, 3027, 32]-code) [i]✔
40Linear OA(5132, 3167, F5, 30) (dual of [3167, 3035, 31]-code) [i]✔
41Linear OA(5140, 3182, F5, 31) (dual of [3182, 3042, 32]-code) [i]✔
42Linear OA(5150, 3158, F5, 34) (dual of [3158, 3008, 35]-code) [i]✔Construction XX with a Chain of Cyclic Codes
43Linear OA(5130, 3158, F5, 29) (dual of [3158, 3028, 30]-code) [i]✔
44Linear OA(5128, 3156, F5, 28) (dual of [3156, 3028, 29]-code) [i]✔
45Linear OOA(5121, 1563, F5, 2, 31) (dual of [(1563, 2), 3005, 32]-NRT-code) [i]OOA Folding
46Linear OOA(5121, 1042, F5, 3, 31) (dual of [(1042, 3), 3005, 32]-NRT-code) [i]