Information on Result #678805
Linear OA(4249, 65570, F4, 41) (dual of [65570, 65321, 42]-code), using construction XX applied to Ce(40) ⊂ Ce(36) ⊂ Ce(34) 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(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(4209, 65536, F4, 35) (dual of [65536, 65327, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(45, 31, F4, 3) (dual of [31, 26, 4]-code or 31-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(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), 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(4249, 34546, F4, 2, 41) (dual of [(34546, 2), 68843, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4249, 34546, F4, 3, 41) (dual of [(34546, 3), 103389, 42]-NRT-code) | [i] | ||
| 3 | Digital (208, 249, 34546)-net over F4 | [i] | ||
| 4 | Linear OOA(4249, 32785, F4, 2, 41) (dual of [(32785, 2), 65321, 42]-NRT-code) | [i] | OOA Folding | |