Information on Result #1749468
Digital (60, 74, 443)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(274, 443, F2, 2, 14) (dual of [(443, 2), 812, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(274, 523, F2, 2, 14) (dual of [(523, 2), 972, 15]-NRT-code), using
- strength reduction [i] based on linear OOA(274, 523, F2, 2, 15) (dual of [(523, 2), 972, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(274, 1046, F2, 15) (dual of [1046, 972, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(274, 1047, F2, 15) (dual of [1047, 973, 16]-code), using
- adding a parity check bit [i] based on linear OA(273, 1046, F2, 14) (dual of [1046, 973, 15]-code), using
- construction XX applied to C1 = C([1021,10]), C2 = C([1,12]), C3 = C1 + C2 = C([1,10]), and C∩ = C1 ∩ C2 = C([1021,12]) [i] based on
- linear OA(261, 1023, F2, 13) (dual of [1023, 962, 14]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(260, 1023, F2, 12) (dual of [1023, 963, 13]-code), using 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(271, 1023, F2, 15) (dual of [1023, 952, 16]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(250, 1023, F2, 10) (dual of [1023, 973, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, 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
- 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([1021,10]), C2 = C([1,12]), C3 = C1 + C2 = C([1,10]), and C∩ = C1 ∩ C2 = C([1021,12]) [i] based on
- adding a parity check bit [i] based on linear OA(273, 1046, F2, 14) (dual of [1046, 973, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(274, 1047, F2, 15) (dual of [1047, 973, 16]-code), using
- OOA 2-folding [i] based on linear OA(274, 1046, F2, 15) (dual of [1046, 972, 16]-code), using
- strength reduction [i] based on linear OOA(274, 523, F2, 2, 15) (dual of [(523, 2), 972, 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.