Information on Result #1313123
Linear OA(957, 779, F9, 20) (dual of [779, 722, 21]-code), using 40 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 9 times 0, 1, 26 times 0) based on linear OA(953, 735, F9, 20) (dual of [735, 682, 21]-code), using
- construction XX applied to C1 = C([73,91]), C2 = C([75,92]), C3 = C1 + C2 = C([75,91]), and C∩ = C1 ∩ C2 = C([73,92]) [i] based on
- linear OA(949, 728, F9, 19) (dual of [728, 679, 20]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {73,74,…,91}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(949, 728, F9, 18) (dual of [728, 679, 19]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {75,76,…,92}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(952, 728, F9, 20) (dual of [728, 676, 21]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {73,74,…,92}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(946, 728, F9, 17) (dual of [728, 682, 18]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {75,76,…,91}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(91, 4, F9, 1) (dual of [4, 3, 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: 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(957, 779, F9, 2, 20) (dual of [(779, 2), 1501, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(957, 779, F9, 3, 20) (dual of [(779, 3), 2280, 21]-NRT-code) | [i] | ||
| 3 | Digital (37, 57, 779)-net over F9 | [i] | ||