Information on Result #714485
Linear OA(839, 82, F8, 20) (dual of [82, 43, 21]-code), using construction XX applied to C1 = C([0,18]), C2 = C([7,19]), C3 = C1 + C2 = C([7,18]), 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(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 = {7,8,…,19}, and designed minimum distance d ≥ |I|+1 = 14 [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(820, 63, F8, 12) (dual of [63, 43, 13]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {7,8,…,18}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(88, 17, F8, 6) (dual of [17, 9, 7]-code), using
- extended algebraic-geometric code AGe(F,10P) [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, 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(839, 41, F8, 2, 20) (dual of [(41, 2), 43, 21]-NRT-code) | [i] | OOA Folding | |