Information on Result #1315263
Linear OA(3262, 1340, F32, 27) (dual of [1340, 1278, 28]-code), using 304 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 7 times 0, 1, 18 times 0, 1, 44 times 0, 1, 87 times 0, 1, 140 times 0) based on linear OA(3253, 1027, F32, 27) (dual of [1027, 974, 28]-code), using
- construction XX applied to C1 = C([1022,24]), C2 = C([0,25]), C3 = C1 + C2 = C([0,24]), and C∩ = C1 ∩ C2 = C([1022,25]) [i] based on
- linear OA(3251, 1023, F32, 26) (dual of [1023, 972, 27]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,24}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(3251, 1023, F32, 26) (dual of [1023, 972, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(3253, 1023, F32, 27) (dual of [1023, 970, 28]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,25}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3249, 1023, F32, 25) (dual of [1023, 974, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [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)
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(3262, 1340, F32, 2, 27) (dual of [(1340, 2), 2618, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (35, 62, 1340)-net over F32 | [i] | ||
| 3 | Linear OOA(3262, 670, F32, 2, 27) (dual of [(670, 2), 1278, 28]-NRT-code) | [i] | OOA Folding | |