Information on Result #678801
Linear OA(4255, 65567, F4, 42) (dual of [65567, 65312, 43]-code), using construction XX applied to Ce(41) ⊂ Ce(37) ⊂ Ce(36) based on
- linear OA(4249, 65536, F4, 42) (dual of [65536, 65287, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [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(45, 30, F4, 3) (dual of [30, 25, 4]-code or 30-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4255, 34942, F4, 2, 42) (dual of [(34942, 2), 69629, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4255, 34942, F4, 3, 42) (dual of [(34942, 3), 104571, 43]-NRT-code) | [i] | ||
| 3 | Digital (213, 255, 34942)-net over F4 | [i] | ||
| 4 | Linear OOA(4255, 32783, F4, 2, 42) (dual of [(32783, 2), 65311, 43]-NRT-code) | [i] | OOA Folding | |