Information on Result #686987
Linear OA(8160, 32852, F8, 31) (dual of [32852, 32692, 32]-code), using construction X applied to Ce(30) ⊂ Ce(17) based on
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(876, 32768, F8, 18) (dual of [32768, 32692, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(824, 84, F8, 12) (dual of [84, 60, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(824, 130, F8, 12) (dual of [130, 106, 13]-code), using
- trace code [i] based on linear OA(6412, 65, F64, 12) (dual of [65, 53, 13]-code or 65-arc in PG(11,64)), using
- extended Reed–Solomon code RSe(53,64) [i]
- trace code [i] based on linear OA(6412, 65, F64, 12) (dual of [65, 53, 13]-code or 65-arc in PG(11,64)), using
- discarding factors / shortening the dual code based on linear OA(824, 130, F8, 12) (dual of [130, 106, 13]-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 OA(8161, 32853, F8, 31) (dual of [32853, 32692, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8160, 16426, F8, 2, 31) (dual of [(16426, 2), 32692, 32]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8160, 10950, F8, 3, 31) (dual of [(10950, 3), 32690, 32]-NRT-code) | [i] | ||