Information on Result #1720730
Digital (187, 221, 9785)-net over F4, using net defined by OOA based on linear OOA(4221, 9785, F4, 39, 34) (dual of [(9785, 39), 381394, 35]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OOA(4221, 58711, F4, 3, 34) (dual of [(58711, 3), 175912, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4221, 58713, F4, 3, 34) (dual of [(58713, 3), 175918, 35]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4221, 58713, F4, 34) (dual of [58713, 58492, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4221, 65609, F4, 34) (dual of [65609, 65388, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(24) [i] based on
- linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(420, 73, F4, 8) (dual of [73, 53, 9]-code), using
- construction XX applied to C1 = C({0,1,2,3,31,47}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,31,47}) [i] based on
- linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,31,47}, and minimum distance d ≥ |{−2,−1,…,4}|+1 = 8 (BCH-bound) [i]
- linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(419, 63, F4, 8) (dual of [63, 44, 9]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,31,47}, and minimum distance d ≥ |{−2,−1,…,5}|+1 = 9 (BCH-bound) [i]
- linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction XX applied to C1 = C({0,1,2,3,31,47}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,31,47}) [i] based on
- construction X applied to Ce(33) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(4221, 65609, F4, 34) (dual of [65609, 65388, 35]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4221, 58713, F4, 34) (dual of [58713, 58492, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(4221, 58713, F4, 3, 34) (dual of [(58713, 3), 175918, 35]-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.