Information on Result #718937
Linear OA(937, 750, F9, 12) (dual of [750, 713, 13]-code), using construction XX applied to C1 = C([0,9]), C2 = C([5,11]), C3 = C1 + C2 = C([5,9]), and C∩ = C1 ∩ C2 = C([0,11]) based on
- linear OA(925, 728, F9, 10) (dual of [728, 703, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(921, 728, F9, 7) (dual of [728, 707, 8]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {5,6,…,11}, and designed minimum distance d ≥ |I|+1 = 8 [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(915, 728, F9, 5) (dual of [728, 713, 6]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {5,6,7,8,9}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(95, 15, F9, 4) (dual of [15, 10, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(95, 16, F9, 4) (dual of [16, 11, 5]-code), using
- extended algebraic-geometric code AGe(F,11P) [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- discarding factors / shortening the dual code based on linear OA(95, 16, F9, 4) (dual of [16, 11, 5]-code), using
- linear OA(91, 7, F9, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- Reed–Solomon code RS(8,9) [i]
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
Mode: Constructive and 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(937, 375, F9, 2, 12) (dual of [(375, 2), 713, 13]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(937, 250, F9, 3, 12) (dual of [(250, 3), 713, 13]-NRT-code) | [i] | ||