Information on Result #1313053
Linear OA(940, 757, F9, 14) (dual of [757, 717, 15]-code), using 20 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 15 times 0) based on linear OA(937, 734, F9, 14) (dual of [734, 697, 15]-code), using
- construction XX applied to C1 = C([727,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([727,12]) [i] based on
- linear OA(934, 728, F9, 13) (dual of [728, 694, 14]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(934, 728, F9, 13) (dual of [728, 694, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(937, 728, F9, 14) (dual of [728, 691, 15]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(931, 728, F9, 12) (dual of [728, 697, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(90, 3, F9, 0) (dual of [3, 3, 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(940, 757, F9, 2, 14) (dual of [(757, 2), 1474, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(940, 757, F9, 3, 14) (dual of [(757, 3), 2231, 15]-NRT-code) | [i] | ||
| 3 | Digital (26, 40, 757)-net over F9 | [i] | ||
| 4 | Linear OOA(940, 378, F9, 2, 14) (dual of [(378, 2), 716, 15]-NRT-code) | [i] | OOA Folding | |