Information on Result #716127
Linear OA(8117, 546, F8, 41) (dual of [546, 429, 42]-code), using construction XX applied to C1 = C([45,81]), C2 = C([41,75]), C3 = C1 + C2 = C([45,75]), and C∩ = C1 ∩ C2 = C([41,81]) based on
- linear OA(897, 511, F8, 37) (dual of [511, 414, 38]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {45,46,…,81}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(891, 511, F8, 35) (dual of [511, 420, 36]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {41,42,…,75}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8106, 511, F8, 41) (dual of [511, 405, 42]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {41,42,…,81}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(882, 511, F8, 31) (dual of [511, 429, 32]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {45,46,…,75}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(87, 22, F8, 5) (dual of [22, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- linear OA(84, 13, F8, 3) (dual of [13, 9, 4]-code or 13-cap in PG(3,8)), 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(8118, 547, F8, 41) (dual of [547, 429, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8116, 545, F8, 40) (dual of [545, 429, 41]-code) | [i] | Truncation | |
| 3 | Linear OOA(8117, 273, F8, 2, 41) (dual of [(273, 2), 429, 42]-NRT-code) | [i] | OOA Folding | |