Information on Result #1308109
Linear OA(4122, 1147, F4, 31) (dual of [1147, 1025, 32]-code), using 108 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 32 times 0, 1, 42 times 0) based on linear OA(4116, 1033, F4, 31) (dual of [1033, 917, 32]-code), using
- construction XX applied to C1 = C([1022,28]), C2 = C([0,29]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([1022,29]) [i] based on
- 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 = {−1,0,…,28}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4111, 1023, F4, 30) (dual of [1023, 912, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4116, 1023, F4, 31) (dual of [1023, 907, 32]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,29}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(4106, 1023, F4, 29) (dual of [1023, 917, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- 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
- linear OA(40, 5, F4, 0) (dual of [5, 5, 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(4122, 1147, F4, 2, 31) (dual of [(1147, 2), 2172, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4122, 1147, F4, 3, 31) (dual of [(1147, 3), 3319, 32]-NRT-code) | [i] | ||
| 3 | Digital (91, 122, 1147)-net over F4 | [i] | ||
| 4 | Linear OOA(4122, 573, F4, 2, 31) (dual of [(573, 2), 1024, 32]-NRT-code) | [i] | OOA Folding | |