Information on Result #1752354
Digital (124, 154, 503)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2154, 503, F2, 2, 30) (dual of [(503, 2), 852, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2154, 523, F2, 2, 30) (dual of [(523, 2), 892, 31]-NRT-code), using
- strength reduction [i] based on linear OOA(2154, 523, F2, 2, 31) (dual of [(523, 2), 892, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2154, 1046, F2, 31) (dual of [1046, 892, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2154, 1047, F2, 31) (dual of [1047, 893, 32]-code), using
- adding a parity check bit [i] based on linear OA(2153, 1046, F2, 30) (dual of [1046, 893, 31]-code), using
- construction XX applied to C1 = C([1021,26]), C2 = C([1,28]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C([1021,28]) [i] based on
- linear OA(2141, 1023, F2, 29) (dual of [1023, 882, 30]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,26}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2140, 1023, F2, 28) (dual of [1023, 883, 29]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2151, 1023, F2, 31) (dual of [1023, 872, 32]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2130, 1023, F2, 26) (dual of [1023, 893, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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([1021,26]), C2 = C([1,28]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C([1021,28]) [i] based on
- adding a parity check bit [i] based on linear OA(2153, 1046, F2, 30) (dual of [1046, 893, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2154, 1047, F2, 31) (dual of [1047, 893, 32]-code), using
- OOA 2-folding [i] based on linear OA(2154, 1046, F2, 31) (dual of [1046, 892, 32]-code), using
- strength reduction [i] based on linear OOA(2154, 523, F2, 2, 31) (dual of [(523, 2), 892, 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.