Information on Result #1709310
Digital (57, 72, 344)-net over F2, using net defined by OOA based on linear OOA(272, 344, F2, 21, 15) (dual of [(344, 21), 7152, 16]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(272, 345, F2, 7, 15) (dual of [(345, 7), 2343, 16]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(272, 345, F2, 3, 15) (dual of [(345, 3), 963, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(272, 1035, F2, 15) (dual of [1035, 963, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(271, 1024, F2, 15) (dual of [1024, 953, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(261, 1024, F2, 13) (dual of [1024, 963, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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(14) ⊂ Ce(12) [i] based on
- OOA 3-folding [i] based on linear OA(272, 1035, F2, 15) (dual of [1035, 963, 16]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(272, 345, F2, 3, 15) (dual of [(345, 3), 963, 16]-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.