Information on Result #1307460
Linear OA(423, 273, F4, 7) (dual of [273, 250, 8]-code), using 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) based on linear OA(422, 266, F4, 7) (dual of [266, 244, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(421, 256, F4, 7) (dual of [256, 235, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(413, 256, F4, 5) (dual of [256, 243, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(49, 10, F4, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,4)), using
- dual of repetition code with length 10 [i]
- linear OA(41, 10, F4, 1) (dual of [10, 9, 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
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, 273, F4, 2, 7) (dual of [(273, 2), 523, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(423, 273, F4, 3, 7) (dual of [(273, 3), 796, 8]-NRT-code) | [i] | ||
| 3 | Digital (16, 23, 273)-net over F4 | [i] | ||