Information on Result #714519
Linear OA(840, 81, F8, 21) (dual of [81, 41, 22]-code), using construction XX applied to C1 = C([0,18]), C2 = C([6,20]), C3 = C1 + C2 = C([6,18]), and C∩ = C1 ∩ C2 = C([0,20]) based on
- linear OA(829, 63, F8, 19) (dual of [63, 34, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(826, 63, F8, 15) (dual of [63, 37, 16]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {6,7,…,20}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(833, 63, F8, 21) (dual of [63, 30, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(822, 63, F8, 13) (dual of [63, 41, 14]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {6,7,…,18}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(86, 13, F8, 5) (dual of [13, 7, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 14, F8, 5) (dual of [14, 8, 6]-code), using
- extended algebraic-geometric code AGe(F,8P) [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(86, 14, F8, 5) (dual of [14, 8, 6]-code), using
- linear OA(81, 5, F8, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- Reed–Solomon code RS(7,8) [i]
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-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.