Information on Result #1307454
Linear OA(423, 1039, F4, 6) (dual of [1039, 1016, 7]-code), using 4 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0) based on linear OA(422, 1034, F4, 6) (dual of [1034, 1012, 7]-code), using
- construction XX applied to C1 = C([337,341]), C2 = C([339,342]), C3 = C1 + C2 = C([339,341]), and C∩ = C1 ∩ C2 = C([337,342]) [i] based on
- linear OA(416, 1023, F4, 5) (dual of [1023, 1007, 6]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {337,338,339,340,341}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(416, 1023, F4, 4) (dual of [1023, 1007, 5]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {339,340,341,342}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(421, 1023, F4, 6) (dual of [1023, 1002, 7]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {337,338,…,342}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(411, 1023, F4, 3) (dual of [1023, 1012, 4]-code or 1023-cap in PG(10,4)), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {339,340,341}, and designed minimum distance d ≥ |I|+1 = 4 [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: 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(423, 1039, F4, 2, 6) (dual of [(1039, 2), 2055, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(423, 1039, F4, 3, 6) (dual of [(1039, 3), 3094, 7]-NRT-code) | [i] | ||
| 3 | Digital (17, 23, 1039)-net over F4 | [i] | ||
| 4 | Linear OOA(423, 519, F4, 2, 6) (dual of [(519, 2), 1015, 7]-NRT-code) | [i] | OOA Folding | |