Information on Result #716394
Linear OA(8133, 544, F8, 47) (dual of [544, 411, 48]-code), using construction XX applied to C1 = C([505,37]), C2 = C([0,40]), C3 = C1 + C2 = C([0,37]), and C∩ = C1 ∩ C2 = C([505,40]) based on
- linear OA(8118, 511, F8, 44) (dual of [511, 393, 45]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−6,−5,…,37}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(8106, 511, F8, 41) (dual of [511, 405, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- 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 = {−6,−5,…,40}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(8100, 511, F8, 38) (dual of [511, 411, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [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(8134, 545, F8, 47) (dual of [545, 411, 48]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8133, 272, F8, 2, 47) (dual of [(272, 2), 411, 48]-NRT-code) | [i] | OOA Folding | |