Information on Result #731615
Linear OA(1688, 131096, F16, 21) (dual of [131096, 131008, 22]-code), using trace code based on linear OA(25644, 65548, F256, 21) (dual of [65548, 65504, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(1689, 131097, F16, 21) (dual of [131097, 131008, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1688, 131096, F16, 2, 21) (dual of [(131096, 2), 262104, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (67, 88, 131096)-net over F16 | [i] | ||
| 4 | Linear OA(1689, 131098, F16, 21) (dual of [131098, 131009, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(1688, 65548, F16, 2, 21) (dual of [(65548, 2), 131008, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(1688, 13109, F16, 21, 21) (dual of [(13109, 21), 275201, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |