Information on Result #1809841
Digital (54, 100, 1281)-net over F32, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(32100, 1281, F32, 46) (dual of [1281, 1181, 47]-code), using
- 242 step Varšamov–Edel lengthening with (ri) = (5, 1, 0, 0, 1, 4 times 0, 1, 12 times 0, 1, 23 times 0, 1, 42 times 0, 1, 66 times 0, 1, 85 times 0) [i] based on linear OA(3288, 1027, F32, 46) (dual of [1027, 939, 47]-code), using
- construction XX applied to C1 = C([1022,43]), C2 = C([0,44]), C3 = C1 + C2 = C([0,43]), and C∩ = C1 ∩ C2 = C([1022,44]) [i] based on
- linear OA(3286, 1023, F32, 45) (dual of [1023, 937, 46]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,43}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3286, 1023, F32, 45) (dual of [1023, 937, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3288, 1023, F32, 46) (dual of [1023, 935, 47]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,44}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(3284, 1023, F32, 44) (dual of [1023, 939, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([1022,43]), C2 = C([0,44]), C3 = C1 + C2 = C([0,43]), and C∩ = C1 ∩ C2 = C([1022,44]) [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.