Information on Result #714520
Linear OA(834, 71, F8, 20) (dual of [71, 37, 21]-code), using construction XX applied to C1 = C([0,18]), C2 = C([4,19]), C3 = C1 + C2 = C([4,18]), and C∩ = C1 ∩ C2 = C([0,19]) 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(828, 63, F8, 16) (dual of [63, 35, 17]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {4,5,…,19}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(831, 63, F8, 20) (dual of [63, 32, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [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 = {4,5,…,18}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(83, 6, F8, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,8) or 6-cap in PG(2,8)), using
- discarding factors / shortening the dual code based on linear OA(83, 8, F8, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,8) or 8-cap in PG(2,8)), using
- Reed–Solomon code RS(5,8) [i]
- discarding factors / shortening the dual code based on linear OA(83, 8, F8, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,8) or 8-cap in PG(2,8)), using
- linear OA(80, 2, F8, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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.