Information on Result #1773054
Digital (50, 65, 1286)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(465, 1286, F4, 15) (dual of [1286, 1221, 16]-code), using
- 244 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 11 times 0, 1, 22 times 0, 1, 40 times 0, 1, 64 times 0, 1, 92 times 0) [i] based on linear OA(456, 1033, F4, 15) (dual of [1033, 977, 16]-code), using
- construction XX applied to C1 = C([1022,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([1022,13]) [i] based on
- linear OA(451, 1023, F4, 14) (dual of [1023, 972, 15]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(451, 1023, F4, 14) (dual of [1023, 972, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(456, 1023, F4, 15) (dual of [1023, 967, 16]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(446, 1023, F4, 13) (dual of [1023, 977, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(40, 5, F4, 0) (dual of [5, 5, 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
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code) (see above)
- construction XX applied to C1 = C([1022,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([1022,13]) [i] based on
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.