Information on Result #722462
Linear OA(1699, 268, F16, 56) (dual of [268, 169, 57]-code), using construction X applied to C([101,156]) ⊂ C([103,154]) based on
- linear OA(1696, 257, F16, 56) (dual of [257, 161, 57]-code), using the BCH-code C(I) with length 257 | 164−1, defining interval I = {101,102,…,156}, and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(1688, 257, F16, 52) (dual of [257, 169, 53]-code), using the BCH-code C(I) with length 257 | 164−1, defining interval I = {103,104,…,154}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(163, 11, F16, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,16) or 11-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), 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(1699, 268, F16, 55) (dual of [268, 169, 56]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(16101, 270, F16, 56) (dual of [270, 169, 57]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(1698, 267, F16, 55) (dual of [267, 169, 56]-code) | [i] | Truncation | |
| 4 | Linear OA(16101, 271, F16, 56) (dual of [271, 170, 57]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(16102, 273, F16, 56) (dual of [273, 171, 57]-code) | [i] | ||
| 6 | Linear OOA(1699, 134, F16, 2, 56) (dual of [(134, 2), 169, 57]-NRT-code) | [i] | OOA Folding | |