Information on Result #1543254
Linear OOA(4223, 38472, F4, 3, 36) (dual of [(38472, 3), 115193, 37]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4223, 38472, F4, 36) (dual of [38472, 38249, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4223, 65567, F4, 36) (dual of [65567, 65344, 37]-code), using
- 1 times truncation [i] based on linear OA(4224, 65568, F4, 37) (dual of [65568, 65344, 38]-code), using
- construction XX applied to Ce(36) ⊂ Ce(32) ⊂ Ce(30) [i] based on
- 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(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(36) ⊂ Ce(32) ⊂ Ce(30) [i] based on
- 1 times truncation [i] based on linear OA(4224, 65568, F4, 37) (dual of [65568, 65344, 38]-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(4223, 6411, F4, 39, 36) (dual of [(6411, 39), 249806, 37]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |