Information on Result #1711678
Digital (159, 190, 644)-net over F2, using net defined by OOA based on linear OOA(2190, 644, F2, 40, 31) (dual of [(644, 40), 25570, 32]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2190, 1289, F2, 8, 31) (dual of [(1289, 8), 10122, 32]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2190, 1289, F2, 3, 31) (dual of [(1289, 3), 3677, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2190, 1376, F2, 3, 31) (dual of [(1376, 3), 3938, 32]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2189, 1376, F2, 3, 31) (dual of [(1376, 3), 3939, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2189, 4128, F2, 31) (dual of [4128, 3939, 32]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2187, 4126, F2, 31) (dual of [4126, 3939, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(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(30) ⊂ Ce(26) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2187, 4126, F2, 31) (dual of [4126, 3939, 32]-code), using
- OOA 3-folding [i] based on linear OA(2189, 4128, F2, 31) (dual of [4128, 3939, 32]-code), using
- 21 times duplication [i] based on linear OOA(2189, 1376, F2, 3, 31) (dual of [(1376, 3), 3939, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2190, 1376, F2, 3, 31) (dual of [(1376, 3), 3938, 32]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2190, 1289, F2, 3, 31) (dual of [(1289, 3), 3677, 32]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.