Information on Result #720391
Linear OA(998, 738, F9, 36) (dual of [738, 640, 37]-code), using construction XX applied to C1 = C([726,32]), C2 = C([0,33]), C3 = C1 + C2 = C([0,32]), and C∩ = C1 ∩ C2 = C([726,33]) based on
- linear OA(994, 728, F9, 35) (dual of [728, 634, 36]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−2,−1,…,32}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(991, 728, F9, 34) (dual of [728, 637, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(997, 728, F9, 36) (dual of [728, 631, 37]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−2,−1,…,33}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(988, 728, F9, 33) (dual of [728, 640, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- 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
- 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
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(998, 369, F9, 2, 36) (dual of [(369, 2), 640, 37]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(998, 246, F9, 3, 36) (dual of [(246, 3), 640, 37]-NRT-code) | [i] | ||