Information on Result #687394
Linear OA(8157, 4148, F8, 41) (dual of [4148, 3991, 42]-code), using construction X applied to Ce(40) ⊂ Ce(29) based on
- linear OA(8141, 4096, F8, 41) (dual of [4096, 3955, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(8105, 4096, F8, 30) (dual of [4096, 3991, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(816, 52, F8, 10) (dual of [52, 36, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(816, 63, F8, 10) (dual of [63, 47, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(816, 63, F8, 10) (dual of [63, 47, 11]-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(8158, 4149, F8, 41) (dual of [4149, 3991, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8156, 4147, F8, 40) (dual of [4147, 3991, 41]-code) | [i] | Truncation | |
| 3 | Linear OOA(8157, 2074, F8, 2, 41) (dual of [(2074, 2), 3991, 42]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(8157, 1382, F8, 3, 41) (dual of [(1382, 3), 3989, 42]-NRT-code) | [i] | ||