Information on Result #1307530
Linear OA(439, 271, F4, 12) (dual of [271, 232, 13]-code), using 2 step Varšamov–Edel lengthening with (ri) = (1, 0) based on linear OA(438, 268, F4, 12) (dual of [268, 230, 13]-code), using
- construction XX applied to C1 = C([253,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([253,9]) [i] based on
- linear OA(433, 255, F4, 11) (dual of [255, 222, 12]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(429, 255, F4, 10) (dual of [255, 226, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(437, 255, F4, 12) (dual of [255, 218, 13]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,9}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(425, 255, F4, 9) (dual of [255, 230, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(41, 9, F4, 1) (dual of [9, 8, 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(439, 271, F4, 2, 12) (dual of [(271, 2), 503, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(439, 271, F4, 3, 12) (dual of [(271, 3), 774, 13]-NRT-code) | [i] | ||
| 3 | Digital (27, 39, 271)-net over F4 | [i] | ||