Information on Result #679376
Linear OA(471, 16413, F4, 13) (dual of [16413, 16342, 14]-code), using construction XX applied to Ce(12) ⊂ Ce(8) ⊂ Ce(6) based on
- linear OA(464, 16384, F4, 13) (dual of [16384, 16320, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(443, 16384, F4, 9) (dual of [16384, 16341, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(436, 16384, F4, 7) (dual of [16384, 16348, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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]
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 OA(470, 16412, F4, 12) (dual of [16412, 16342, 13]-code) | [i] | Truncation | |
| 2 | Linear OOA(471, 5471, F4, 3, 13) (dual of [(5471, 3), 16342, 14]-NRT-code) | [i] | OOA Folding | |