Information on Result #716021
Linear OA(8112, 544, F8, 39) (dual of [544, 432, 40]-code), using construction XX applied to C1 = C([505,29]), C2 = C([0,32]), C3 = C1 + C2 = C([0,29]), and C∩ = C1 ∩ C2 = C([505,32]) based on
- linear OA(897, 511, F8, 36) (dual of [511, 414, 37]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−6,−5,…,29}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(885, 511, F8, 33) (dual of [511, 426, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8103, 511, F8, 39) (dual of [511, 408, 40]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−6,−5,…,32}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(879, 511, F8, 30) (dual of [511, 432, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(87, 25, F8, 5) (dual of [25, 18, 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(8113, 545, F8, 39) (dual of [545, 432, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8112, 272, F8, 2, 39) (dual of [(272, 2), 432, 40]-NRT-code) | [i] | OOA Folding | |