Information on Result #681863
Linear OA(431, 263, F4, 10) (dual of [263, 232, 11]-code), using construction XX applied to Ce(9) ⊂ Ce(8) ⊂ Ce(6) based on
- linear OA(429, 256, F4, 10) (dual of [256, 227, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(425, 256, F4, 9) (dual of [256, 231, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 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(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(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(431, 222, F4, 2, 10) (dual of [(222, 2), 413, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(431, 222, F4, 3, 10) (dual of [(222, 3), 635, 11]-NRT-code) | [i] | ||
| 3 | Digital (21, 31, 222)-net over F4 | [i] | ||