Information on Result #1692646
Linear OOA(249, 1754, F2, 8, 8) (dual of [(1754, 8), 13983, 9]-NRT-code), using appending kth column based on linear OOA(249, 1754, F2, 7, 8) (dual of [(1754, 7), 12229, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(249, 1754, F2, 2, 8) (dual of [(1754, 2), 3459, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(249, 2054, F2, 2, 8) (dual of [(2054, 2), 4059, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(249, 4108, F2, 8) (dual of [4108, 4059, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(249, 4109, F2, 8) (dual of [4109, 4060, 9]-code), using
- 1 times truncation [i] based on linear OA(250, 4110, F2, 9) (dual of [4110, 4060, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(249, 4096, F2, 9) (dual of [4096, 4047, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(237, 4096, F2, 7) (dual of [4096, 4059, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(213, 14, F2, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,2)), using
- dual of repetition code with length 14 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- 1 times truncation [i] based on linear OA(250, 4110, F2, 9) (dual of [4110, 4060, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(249, 4109, F2, 8) (dual of [4109, 4060, 9]-code), using
- OOA 2-folding [i] based on linear OA(249, 4108, F2, 8) (dual of [4108, 4059, 9]-code), using
- discarding factors / shortening the dual code based on linear OOA(249, 2054, F2, 2, 8) (dual of [(2054, 2), 4059, 9]-NRT-code), 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 | Digital (41, 49, 1754)-net over F2 | [i] | Net Defined by OOA | |