Information on Result #714499
Linear OA(841, 82, F8, 21) (dual of [82, 41, 22]-code), using construction XX applied to C1 = C([62,18]), C2 = C([6,19]), C3 = C1 + C2 = C([6,18]), and C∩ = C1 ∩ C2 = C([62,19]) based on
- linear OA(831, 63, F8, 20) (dual of [63, 32, 21]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [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(833, 63, F8, 21) (dual of [63, 30, 22]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−1,0,…,19}, 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(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(841, 41, F8, 2, 21) (dual of [(41, 2), 41, 22]-NRT-code) | [i] | OOA Folding | |