Information on Result #1315391
Linear OA(3291, 1372, F32, 41) (dual of [1372, 1281, 42]-code), using 330 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 0, 0, 0, 1, 9 times 0, 1, 18 times 0, 1, 35 times 0, 1, 61 times 0, 1, 88 times 0, 1, 107 times 0) based on linear OA(3279, 1030, F32, 41) (dual of [1030, 951, 42]-code), using
- construction XX applied to C1 = C([1021,37]), C2 = C([0,38]), C3 = C1 + C2 = C([0,37]), and C∩ = C1 ∩ C2 = C([1021,38]) [i] based on
- linear OA(3276, 1023, F32, 40) (dual of [1023, 947, 41]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,37}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3274, 1023, F32, 39) (dual of [1023, 949, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3278, 1023, F32, 41) (dual of [1023, 945, 42]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(3272, 1023, F32, 38) (dual of [1023, 951, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- 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
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3291, 1372, F32, 2, 41) (dual of [(1372, 2), 2653, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (50, 91, 1372)-net over F32 | [i] | ||
| 3 | Linear OOA(3291, 686, F32, 2, 41) (dual of [(686, 2), 1281, 42]-NRT-code) | [i] | OOA Folding | |