Information on Result #706019
Linear OA(426, 268, F4, 8) (dual of [268, 242, 9]-code), using construction XX applied to C1 = C([253,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([253,5]) based on
- linear OA(421, 255, F4, 7) (dual of [255, 234, 8]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(417, 255, F4, 6) (dual of [255, 238, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(425, 255, F4, 8) (dual of [255, 230, 9]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−2,−1,…,5}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(413, 255, F4, 5) (dual of [255, 242, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [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: 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(426, 268, F4, 2, 8) (dual of [(268, 2), 510, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(426, 268, F4, 3, 8) (dual of [(268, 3), 778, 9]-NRT-code) | [i] | ||
| 3 | Digital (18, 26, 268)-net over F4 | [i] | ||
| 4 | Linear OA(427, 280, F4, 8) (dual of [280, 253, 9]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OOA(426, 134, F4, 2, 8) (dual of [(134, 2), 242, 9]-NRT-code) | [i] | OOA Folding | |