Information on Result #714891
Linear OA(881, 89, F8, 62) (dual of [89, 8, 63]-code), using construction XX applied to C1 = C([10,62]), C2 = C([1,53]), C3 = C1 + C2 = C([10,53]), and C∩ = C1 ∩ C2 = C([1,62]) based on
- linear OA(859, 63, F8, 53) (dual of [63, 4, 54]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {10,11,…,62}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(859, 63, F8, 53) (dual of [63, 4, 54]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,53], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(862, 63, F8, 62) (dual of [63, 1, 63]-code or 63-arc in PG(61,8)), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,62], and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(854, 63, F8, 44) (dual of [63, 9, 45]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {10,11,…,53}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(89, 13, F8, 8) (dual of [13, 4, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(89, 14, F8, 8) (dual of [14, 5, 9]-code), using
- extended algebraic-geometric code AGe(F,5P) [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- discarding factors / shortening the dual code based on linear OA(89, 14, F8, 8) (dual of [14, 5, 9]-code), using
- linear OA(89, 13, F8, 8) (dual of [13, 4, 9]-code) (see above)
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(879, 87, F8, 60) (dual of [87, 8, 61]-code) | [i] | Truncation | |