Information on Result #714736
Linear OA(868, 97, F8, 37) (dual of [97, 29, 38]-code), using construction XX applied to C1 = C([7,36]), C2 = C([0,26]), C3 = C1 + C2 = C([7,26]), and C∩ = C1 ∩ C2 = C([0,36]) based on
- linear OA(844, 63, F8, 30) (dual of [63, 19, 31]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {7,8,…,36}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(839, 63, F8, 27) (dual of [63, 24, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(849, 63, F8, 37) (dual of [63, 14, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(832, 63, F8, 20) (dual of [63, 31, 21]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {7,8,…,26}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(812, 22, F8, 9) (dual of [22, 10, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(812, 23, F8, 9) (dual of [23, 11, 10]-code), using
- algebraic-geometric code AG(F,13P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- algebraic-geometric code AG(F,13P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OA(812, 23, F8, 9) (dual of [23, 11, 10]-code), using
- linear OA(87, 12, F8, 6) (dual of [12, 5, 7]-code), using
- discarding factors / shortening the dual code based on 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
- discarding factors / shortening the dual code based on linear OA(87, 14, F8, 6) (dual of [14, 7, 7]-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
None.