Information on Result #1710274
Digital (76, 94, 214)-net over F2, using net defined by OOA based on linear OOA(294, 214, F2, 25, 18) (dual of [(214, 25), 5256, 19]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(294, 429, F2, 5, 18) (dual of [(429, 5), 2051, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(294, 430, F2, 5, 18) (dual of [(430, 5), 2056, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(294, 430, F2, 2, 18) (dual of [(430, 2), 766, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(294, 523, F2, 2, 18) (dual of [(523, 2), 952, 19]-NRT-code), using
- strength reduction [i] based on linear OOA(294, 523, F2, 2, 19) (dual of [(523, 2), 952, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(294, 1046, F2, 19) (dual of [1046, 952, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(294, 1047, F2, 19) (dual of [1047, 953, 20]-code), using
- adding a parity check bit [i] based on linear OA(293, 1046, F2, 18) (dual of [1046, 953, 19]-code), using
- construction XX applied to C1 = C([1021,14]), C2 = C([1,16]), C3 = C1 + C2 = C([1,14]), and C∩ = C1 ∩ C2 = C([1021,16]) [i] based on
- linear OA(281, 1023, F2, 17) (dual of [1023, 942, 18]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,14}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(280, 1023, F2, 16) (dual of [1023, 943, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(291, 1023, F2, 19) (dual of [1023, 932, 20]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(270, 1023, F2, 14) (dual of [1023, 953, 15]-code), using 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(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
- 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 (see above)
- construction XX applied to C1 = C([1021,14]), C2 = C([1,16]), C3 = C1 + C2 = C([1,14]), and C∩ = C1 ∩ C2 = C([1021,16]) [i] based on
- adding a parity check bit [i] based on linear OA(293, 1046, F2, 18) (dual of [1046, 953, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(294, 1047, F2, 19) (dual of [1047, 953, 20]-code), using
- OOA 2-folding [i] based on linear OA(294, 1046, F2, 19) (dual of [1046, 952, 20]-code), using
- strength reduction [i] based on linear OOA(294, 523, F2, 2, 19) (dual of [(523, 2), 952, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(294, 523, F2, 2, 18) (dual of [(523, 2), 952, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(294, 430, F2, 2, 18) (dual of [(430, 2), 766, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(294, 430, F2, 5, 18) (dual of [(430, 5), 2056, 19]-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.