Information on Result #1302500
Linear OA(866, 83, F8, 44) (dual of [83, 17, 45]-code), using construction X with Varšamov bound based on
- linear OA(863, 79, F8, 44) (dual of [79, 16, 45]-code), using
- construction XX applied to Ce(44) ⊂ Ce(36) ⊂ Ce(35) [i] based on
- 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(849, 64, F8, 37) (dual of [64, 15, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(848, 64, F8, 36) (dual of [64, 16, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(87, 14, F8, 6) (dual of [14, 7, 7]-code), using
- extended algebraic-geometric code AGe(F,7P) [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(44) ⊂ Ce(36) ⊂ Ce(35) [i] based on
- linear OA(863, 80, F8, 41) (dual of [80, 17, 42]-code), using Gilbert–Varšamov bound and bm = 863 > Vbs−1(k−1) = 398 751911 111861 198501 695716 594673 811062 091043 911989 623402 [i]
- linear OA(82, 3, F8, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,8)), using
- dual of repetition code with length 3 [i]
Mode: 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(867, 85, F8, 44) (dual of [85, 18, 45]-code) | [i] | Construction X with Varšamov Bound | |