Information on Result #714669
Linear OA(852, 82, F8, 30) (dual of [82, 30, 31]-code), using construction XX applied to C1 = C([0,27]), C2 = C([7,29]), C3 = C1 + C2 = C([7,27]), and C∩ = C1 ∩ C2 = C([0,29]) based on
- linear OA(840, 63, F8, 28) (dual of [63, 23, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(837, 63, F8, 23) (dual of [63, 26, 24]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {7,8,…,29}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(844, 63, F8, 30) (dual of [63, 19, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [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 = {7,8,…,27}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(87, 14, F8, 6) (dual of [14, 7, 7]-code), using
- extended algebraic-geometric code AGe(F,7P) [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(852, 41, F8, 2, 30) (dual of [(41, 2), 30, 31]-NRT-code) | [i] | OOA Folding | |