Information on Result #688935
Linear OA(856, 92, F8, 29) (dual of [92, 36, 30]-code), using construction XX applied to Ce(28) ⊂ Ce(18) ⊂ Ce(17) based on
- linear OA(842, 64, F8, 29) (dual of [64, 22, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(829, 64, F8, 19) (dual of [64, 35, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(828, 64, F8, 18) (dual of [64, 36, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(813, 27, F8, 9) (dual of [27, 14, 10]-code), using
- construction X applied to AG(F,7P) ⊂ AG(F,8P) [i] based on
- linear OA(812, 24, F8, 9) (dual of [24, 12, 10]-code), using algebraic-geometric code AG(F,7P) with degPÂ =Â 2 [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using the Klein quartic over F8 [i]
- linear OA(810, 24, F8, 7) (dual of [24, 14, 8]-code), using algebraic-geometric code AG(F,8P) with degPÂ =Â 2 [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24 (see above)
- linear OA(81, 3, F8, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,7P) ⊂ AG(F,8P) [i] based on
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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.
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 OOA(856, 46, F8, 2, 29) (dual of [(46, 2), 36, 30]-NRT-code) | [i] | OOA Folding | |