Information on Result #1749064
Digital (32, 45, 71)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(245, 71, F2, 2, 13) (dual of [(71, 2), 97, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(245, 142, F2, 13) (dual of [142, 97, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(245, 143, F2, 13) (dual of [143, 98, 14]-code), using
- construction XX applied to C1 = C({0,1,3,5,7,63}), C2 = C([0,9]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,63}) [i] based on
- linear OA(236, 127, F2, 11) (dual of [127, 91, 12]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,63}, and minimum distance d ≥ |{−2,−1,…,8}|+1 = 12 (BCH-bound) [i]
- linear OA(236, 127, F2, 11) (dual of [127, 91, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(243, 127, F2, 13) (dual of [127, 84, 14]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,63}, and minimum distance d ≥ |{−2,−1,…,10}|+1 = 14 (BCH-bound) [i]
- linear OA(229, 127, F2, 9) (dual of [127, 98, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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, 8, F2, 1) (dual of [8, 7, 2]-code) (see above)
- construction XX applied to C1 = C({0,1,3,5,7,63}), C2 = C([0,9]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,63}) [i] based on
- discarding factors / shortening the dual code based on linear OA(245, 143, F2, 13) (dual of [143, 98, 14]-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.