Information on Result #714497
Linear OA(837, 78, F8, 20) (dual of [78, 41, 21]-code), using construction XX applied to C1 = C([0,18]), C2 = C([6,19]), C3 = C1 + C2 = C([6,18]), 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(824, 63, F8, 14) (dual of [63, 39, 15]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {6,7,…,19}, and designed minimum distance d ≥ |I|+1 = 15 [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(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(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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(837, 39, F8, 2, 20) (dual of [(39, 2), 41, 21]-NRT-code) | [i] | OOA Folding | |