Information on Result #714858
Linear OA(876, 89, F8, 53) (dual of [89, 13, 54]-code), using construction XX applied to C1 = C([9,53]), C2 = C([1,44]), C3 = C1 + C2 = C([9,44]), and C∩ = C1 ∩ C2 = C([1,53]) based on
- linear OA(855, 63, F8, 45) (dual of [63, 8, 46]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {9,10,…,53}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(854, 63, F8, 44) (dual of [63, 9, 45]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [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(848, 63, F8, 36) (dual of [63, 15, 37]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {9,10,…,44}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- 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
- linear OA(88, 12, F8, 7) (dual of [12, 4, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(88, 14, F8, 7) (dual of [14, 6, 8]-code), using
- extended algebraic-geometric code AGe(F,6P) [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14 (see above)
- discarding factors / shortening the dual code based on linear OA(88, 14, F8, 7) (dual of [14, 6, 8]-code), 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.
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(875, 88, F8, 52) (dual of [88, 13, 53]-code) | [i] | Truncation | |
| 2 | Linear OA(874, 87, F8, 51) (dual of [87, 13, 52]-code) | [i] | ||
| 3 | Linear OOA(876, 44, F8, 2, 53) (dual of [(44, 2), 12, 54]-NRT-code) | [i] | OOA Folding | |