Information on Result #1315167
Linear OA(3236, 1471, F32, 15) (dual of [1471, 1435, 16]-code), using 437 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 13 times 0, 1, 44 times 0, 1, 120 times 0, 1, 252 times 0) based on linear OA(3229, 1027, F32, 15) (dual of [1027, 998, 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(3227, 1023, F32, 14) (dual of [1023, 996, 15]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(3227, 1023, F32, 14) (dual of [1023, 996, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(3229, 1023, F32, 15) (dual of [1023, 994, 16]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3225, 1023, F32, 13) (dual of [1023, 998, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [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(3236, 1471, F32, 2, 15) (dual of [(1471, 2), 2906, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (21, 36, 1471)-net over F32 | [i] | ||
| 3 | Linear OOA(3236, 735, F32, 2, 15) (dual of [(735, 2), 1434, 16]-NRT-code) | [i] | OOA Folding | |