Information on Result #678804
Linear OA(4243, 65555, F4, 40) (dual of [65555, 65312, 41]-code), using construction XX applied to Ce(40) ⊂ Ce(37) ⊂ Ce(36) based on
- linear OA(4241, 65536, F4, 41) (dual of [65536, 65295, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(41, 18, F4, 1) (dual of [18, 17, 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, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(4243, 34156, F4, 2, 40) (dual of [(34156, 2), 68069, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4243, 34156, F4, 3, 40) (dual of [(34156, 3), 102225, 41]-NRT-code) | [i] | ||
| 3 | Digital (203, 243, 34156)-net over F4 | [i] | ||
| 4 | Linear OOA(4243, 32777, F4, 2, 40) (dual of [(32777, 2), 65311, 41]-NRT-code) | [i] | OOA Folding | |