Information on Result #688897
Linear OA(883, 92, F8, 62) (dual of [92, 9, 63]-code), using construction XX applied to Ce(62) ⊂ Ce(45) ⊂ Ce(44) based on
- linear OA(863, 64, F8, 63) (dual of [64, 1, 64]-code or 64-arc in PG(62,8)), using an extension Ce(62) of 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(856, 64, F8, 46) (dual of [64, 8, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(855, 64, F8, 45) (dual of [64, 9, 46]-code), using an extension Ce(44) of 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(819, 27, F8, 15) (dual of [27, 8, 16]-code), using
- construction X applied to AG(F,4P) ⊂ AG(F,5P) [i] based on
- linear OA(818, 24, F8, 15) (dual of [24, 6, 16]-code), using algebraic-geometric code AG(F,4P) 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(816, 24, F8, 13) (dual of [24, 8, 14]-code), using algebraic-geometric code AG(F,5P) 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,4P) ⊂ AG(F,5P) [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 OA(881, 90, F8, 60) (dual of [90, 9, 61]-code) | [i] | Truncation | |
| 2 | Linear OOA(883, 46, F8, 2, 62) (dual of [(46, 2), 9, 63]-NRT-code) | [i] | OOA Folding | |