Information on Result #1809877
Digital (53, 101, 1065)-net over F32, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(32101, 1065, F32, 48) (dual of [1065, 964, 49]-code), using
- discarding factors / shortening the dual code based on linear OA(32101, 1088, F32, 48) (dual of [1088, 987, 49]-code), using
- 52 step Varšamov–Edel lengthening with (ri) = (5, 1, 0, 0, 1, 6 times 0, 1, 13 times 0, 1, 26 times 0) [i] based on linear OA(3292, 1027, F32, 48) (dual of [1027, 935, 49]-code), using
- construction XX applied to C1 = C([1022,45]), C2 = C([0,46]), C3 = C1 + C2 = C([0,45]), and C∩ = C1 ∩ C2 = C([1022,46]) [i] based on
- linear OA(3290, 1023, F32, 47) (dual of [1023, 933, 48]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,45}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(3290, 1023, F32, 47) (dual of [1023, 933, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(3292, 1023, F32, 48) (dual of [1023, 931, 49]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,46}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(3288, 1023, F32, 46) (dual of [1023, 935, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [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([1022,45]), C2 = C([0,46]), C3 = C1 + C2 = C([0,45]), and C∩ = C1 ∩ C2 = C([1022,46]) [i] based on
- 52 step Varšamov–Edel lengthening with (ri) = (5, 1, 0, 0, 1, 6 times 0, 1, 13 times 0, 1, 26 times 0) [i] based on linear OA(3292, 1027, F32, 48) (dual of [1027, 935, 49]-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.