Information on Result #708256
Linear OA(4112, 1034, F4, 30) (dual of [1034, 922, 31]-code), using construction XX applied to C1 = C([313,341]), C2 = C([315,342]), C3 = C1 + C2 = C([315,341]), and C∩ = C1 ∩ C2 = C([313,342]) based on
- linear OA(4106, 1023, F4, 29) (dual of [1023, 917, 30]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {313,314,…,341}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4106, 1023, F4, 28) (dual of [1023, 917, 29]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {315,316,…,342}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4111, 1023, F4, 30) (dual of [1023, 912, 31]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {313,314,…,342}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4101, 1023, F4, 27) (dual of [1023, 922, 28]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {315,316,…,341}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(41, 6, F4, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 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(4112, 897, F4, 2, 30) (dual of [(897, 2), 1682, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4112, 897, F4, 3, 30) (dual of [(897, 3), 2579, 31]-NRT-code) | [i] | ||
| 3 | Digital (82, 112, 897)-net over F4 | [i] | ||
| 4 | Linear OA(4115, 1047, F4, 30) (dual of [1047, 932, 31]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(4116, 1062, F4, 30) (dual of [1062, 946, 31]-code) | [i] | ||
| 6 | Linear OA(4117, 1087, F4, 30) (dual of [1087, 970, 31]-code) | [i] | ||
| 7 | Linear OOA(4112, 517, F4, 2, 30) (dual of [(517, 2), 922, 31]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4112, 344, F4, 3, 30) (dual of [(344, 3), 920, 31]-NRT-code) | [i] | ||