Information on Result #707623
Linear OA(452, 1034, F4, 14) (dual of [1034, 982, 15]-code), using construction XX applied to C1 = C([329,341]), C2 = C([331,342]), C3 = C1 + C2 = C([331,341]), and C∩ = C1 ∩ C2 = C([329,342]) based on
- linear OA(446, 1023, F4, 13) (dual of [1023, 977, 14]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {329,330,…,341}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(446, 1023, F4, 12) (dual of [1023, 977, 13]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {331,332,…,342}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(451, 1023, F4, 14) (dual of [1023, 972, 15]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {329,330,…,342}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(441, 1023, F4, 11) (dual of [1023, 982, 12]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {331,332,…,341}, and designed minimum distance d ≥ |I|+1 = 12 [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(452, 630, F4, 2, 14) (dual of [(630, 2), 1208, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(452, 630, F4, 3, 14) (dual of [(630, 3), 1838, 15]-NRT-code) | [i] | ||
| 3 | Digital (38, 52, 630)-net over F4 | [i] | ||
| 4 | Linear OA(457, 1061, F4, 14) (dual of [1061, 1004, 15]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(458, 1085, F4, 14) (dual of [1085, 1027, 15]-code) | [i] | ||
| 6 | Linear OOA(452, 517, F4, 2, 14) (dual of [(517, 2), 982, 15]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(452, 344, F4, 3, 14) (dual of [(344, 3), 980, 15]-NRT-code) | [i] | ||