Information on Result #1303848
Linear OA(16129, 131098, F16, 31) (dual of [131098, 130969, 32]-code), using construction X with Varšamov bound based on
- linear OA(16128, 131096, F16, 31) (dual of [131096, 130968, 32]-code), using
- trace code [i] based on linear OA(25664, 65548, F256, 31) (dual of [65548, 65484, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- linear OA(25661, 65537, F256, 31) (dual of [65537, 65476, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- trace code [i] based on linear OA(25664, 65548, F256, 31) (dual of [65548, 65484, 32]-code), using
- linear OA(16128, 131097, F16, 30) (dual of [131097, 130969, 31]-code), using Gilbert–Varšamov bound and bm = 16128 > Vbs−1(k−1) = 37 056362 463236 624514 311686 718584 227136 252876 479635 337228 892911 003355 678233 710352 366450 233347 699212 822441 680492 811551 205159 319964 640523 645029 460230 946816 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(16129, 131098, F16, 2, 31) (dual of [(131098, 2), 262067, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (98, 129, 131098)-net over F16 | [i] | ||
| 3 | Linear OOA(16129, 65549, F16, 2, 31) (dual of [(65549, 2), 130969, 32]-NRT-code) | [i] | OOA Folding | |