Information on Result #1424168
Linear OOA(4154, 12256, F4, 2, 28) (dual of [(12256, 2), 24358, 29]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4154, 12256, F4, 28) (dual of [12256, 12102, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4154, 16412, F4, 28) (dual of [16412, 16258, 29]-code), using
- 1 times truncation [i] based on linear OA(4155, 16413, F4, 29) (dual of [16413, 16258, 30]-code), using
- construction XX applied to Ce(28) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(45, 27, F4, 3) (dual of [27, 22, 4]-code or 27-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(28) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(4155, 16413, F4, 29) (dual of [16413, 16258, 30]-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(4154, 6128, F4, 3, 28) (dual of [(6128, 3), 18230, 29]-NRT-code) | [i] | OOA Folding | |