Information on Result #716539
Linear OA(8139, 541, F8, 50) (dual of [541, 402, 51]-code), using construction XX applied to C1 = C([35,81]), C2 = C([32,75]), C3 = C1 + C2 = C([35,75]), and C∩ = C1 ∩ C2 = C([32,81]) based on
- linear OA(8124, 511, F8, 47) (dual of [511, 387, 48]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {35,36,…,81}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(8115, 511, F8, 44) (dual of [511, 396, 45]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {32,33,…,75}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(8130, 511, F8, 50) (dual of [511, 381, 51]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {32,33,…,81}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(8109, 511, F8, 41) (dual of [511, 402, 42]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {35,36,…,75}, and designed minimum distance d ≥ |I|+1 = 42 [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(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
- Reed–Solomon code RS(6,8) [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(8140, 542, F8, 50) (dual of [542, 402, 51]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8139, 270, F8, 2, 50) (dual of [(270, 2), 401, 51]-NRT-code) | [i] | OOA Folding | |