Information on Result #1691450
Linear OOA(2163, 684, F2, 8, 26) (dual of [(684, 8), 5309, 27]-NRT-code), using OOA 2-folding based on linear OOA(2163, 1368, F2, 4, 26) (dual of [(1368, 4), 5309, 27]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2163, 1368, F2, 3, 26) (dual of [(1368, 3), 3941, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2163, 1375, F2, 3, 26) (dual of [(1375, 3), 3962, 27]-NRT-code), using
- strength reduction [i] based on linear OOA(2163, 1375, F2, 3, 27) (dual of [(1375, 3), 3962, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2163, 4125, F2, 27) (dual of [4125, 3962, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2163, 4126, F2, 27) (dual of [4126, 3963, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2157, 4096, F2, 27) (dual of [4096, 3939, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2133, 4096, F2, 23) (dual of [4096, 3963, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(2163, 4126, F2, 27) (dual of [4126, 3963, 28]-code), using
- OOA 3-folding [i] based on linear OA(2163, 4125, F2, 27) (dual of [4125, 3962, 28]-code), using
- strength reduction [i] based on linear OOA(2163, 1375, F2, 3, 27) (dual of [(1375, 3), 3962, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2163, 1375, F2, 3, 26) (dual of [(1375, 3), 3962, 27]-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
None.