Information on Result #1752908
Digital (132, 164, 520)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2164, 520, F2, 2, 32) (dual of [(520, 2), 876, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2164, 523, F2, 2, 32) (dual of [(523, 2), 882, 33]-NRT-code), using
- strength reduction [i] based on linear OOA(2164, 523, F2, 2, 33) (dual of [(523, 2), 882, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2164, 1046, F2, 33) (dual of [1046, 882, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2164, 1047, F2, 33) (dual of [1047, 883, 34]-code), using
- adding a parity check bit [i] based on linear OA(2163, 1046, F2, 32) (dual of [1046, 883, 33]-code), using
- construction XX applied to C1 = C([1021,28]), C2 = C([1,30]), C3 = C1 + C2 = C([1,28]), and C∩ = C1 ∩ C2 = C([1021,30]) [i] based on
- 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(2150, 1023, F2, 30) (dual of [1023, 873, 31]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2161, 1023, F2, 33) (dual of [1023, 862, 34]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,30}, and designed minimum distance d ≥ |I|+1 = 34 [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(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([1021,28]), C2 = C([1,30]), C3 = C1 + C2 = C([1,28]), and C∩ = C1 ∩ C2 = C([1021,30]) [i] based on
- adding a parity check bit [i] based on linear OA(2163, 1046, F2, 32) (dual of [1046, 883, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2164, 1047, F2, 33) (dual of [1047, 883, 34]-code), using
- OOA 2-folding [i] based on linear OA(2164, 1046, F2, 33) (dual of [1046, 882, 34]-code), using
- strength reduction [i] based on linear OOA(2164, 523, F2, 2, 33) (dual of [(523, 2), 882, 34]-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.