Information on Result #1545535
Linear OOA(4247, 39527, F4, 3, 40) (dual of [(39527, 3), 118334, 41]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4247, 39527, F4, 40) (dual of [39527, 39280, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(4247, 65567, F4, 40) (dual of [65567, 65320, 41]-code), using
- 1 times truncation [i] based on linear OA(4248, 65568, F4, 41) (dual of [65568, 65320, 42]-code), using
- construction XX applied to Ce(40) ⊂ Ce(36) ⊂ Ce(34) [i] 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, 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(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(40) ⊂ Ce(36) ⊂ Ce(34) [i] based on
- 1 times truncation [i] based on linear OA(4248, 65568, F4, 41) (dual of [65568, 65320, 42]-code), 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(4247, 5646, F4, 45, 40) (dual of [(5646, 45), 253823, 41]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |