Information on Result #1307453
Linear OA(419, 269, F4, 6) (dual of [269, 250, 7]-code), using 4 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0) based on linear OA(418, 264, F4, 6) (dual of [264, 246, 7]-code), using
- construction XX applied to C1 = C([81,85]), C2 = C([83,86]), C3 = C1 + C2 = C([83,85]), and C∩ = C1 ∩ C2 = C([81,86]) [i] based on
- linear OA(413, 255, F4, 5) (dual of [255, 242, 6]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {81,82,83,84,85}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(413, 255, F4, 4) (dual of [255, 242, 5]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {83,84,85,86}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(417, 255, F4, 6) (dual of [255, 238, 7]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {81,82,…,86}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(49, 255, F4, 3) (dual of [255, 246, 4]-code or 255-cap in PG(8,4)), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {83,84,85}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(41, 5, F4, 1) (dual of [5, 4, 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, 4, F4, 0) (dual of [4, 4, 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(419, 269, F4, 2, 6) (dual of [(269, 2), 519, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(419, 269, F4, 3, 6) (dual of [(269, 3), 788, 7]-NRT-code) | [i] | ||
| 3 | Digital (13, 19, 269)-net over F4 | [i] | ||