Information on Result #1708762
Digital (55, 68, 606)-net over F2, using net defined by OOA based on linear OOA(268, 606, F2, 18, 13) (dual of [(606, 18), 10840, 14]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(268, 607, F2, 6, 13) (dual of [(607, 6), 3574, 14]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(268, 607, F2, 3, 13) (dual of [(607, 3), 1753, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(268, 686, F2, 3, 13) (dual of [(686, 3), 1990, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(268, 2058, F2, 13) (dual of [2058, 1990, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(268, 2060, F2, 13) (dual of [2060, 1992, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(267, 2048, F2, 13) (dual of [2048, 1981, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(256, 2048, F2, 11) (dual of [2048, 1992, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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 X applied to Ce(12) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(268, 2060, F2, 13) (dual of [2060, 1992, 14]-code), using
- OOA 3-folding [i] based on linear OA(268, 2058, F2, 13) (dual of [2058, 1990, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(268, 686, F2, 3, 13) (dual of [(686, 3), 1990, 14]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(268, 607, F2, 3, 13) (dual of [(607, 3), 1753, 14]-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.