Information on Result #1749306
Digital (53, 65, 518)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(265, 518, F2, 2, 12) (dual of [(518, 2), 971, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(265, 524, F2, 2, 12) (dual of [(524, 2), 983, 13]-NRT-code), using
- strength reduction [i] based on linear OOA(265, 524, F2, 2, 13) (dual of [(524, 2), 983, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(265, 1048, F2, 13) (dual of [1048, 983, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(264, 1047, F2, 13) (dual of [1047, 983, 14]-code), using
- adding a parity check bit [i] based on linear OA(263, 1046, F2, 12) (dual of [1046, 983, 13]-code), using
- construction XX applied to C1 = C([1021,8]), C2 = C([1,10]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([1021,10]) [i] based on
- linear OA(251, 1023, F2, 11) (dual of [1023, 972, 12]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [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(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(240, 1023, F2, 8) (dual of [1023, 983, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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([1021,8]), C2 = C([1,10]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([1021,10]) [i] based on
- adding a parity check bit [i] based on linear OA(263, 1046, F2, 12) (dual of [1046, 983, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(264, 1047, F2, 13) (dual of [1047, 983, 14]-code), using
- OOA 2-folding [i] based on linear OA(265, 1048, F2, 13) (dual of [1048, 983, 14]-code), using
- strength reduction [i] based on linear OOA(265, 524, F2, 2, 13) (dual of [(524, 2), 983, 14]-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.