Information on Result #716404
Linear OA(8117, 523, F8, 44) (dual of [523, 406, 45]-code), using construction XX applied to C1 = C([509,40]), C2 = C([1,41]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([509,41]) based on
- linear OA(8112, 511, F8, 43) (dual of [511, 399, 44]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,40}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(8108, 511, F8, 41) (dual of [511, 403, 42]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [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 = {−2,−1,…,41}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(8105, 511, F8, 40) (dual of [511, 406, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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 OOA(8117, 261, F8, 2, 44) (dual of [(261, 2), 405, 45]-NRT-code) | [i] | OOA Folding | |