Information on Result #717013
Linear OA(8157, 526, F8, 59) (dual of [526, 369, 60]-code), using construction XX applied to C1 = C([17,73]), C2 = C([20,75]), C3 = C1 + C2 = C([20,73]), and C∩ = C1 ∩ C2 = C([17,75]) based on
- linear OA(8148, 511, F8, 57) (dual of [511, 363, 58]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {17,18,…,73}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(8148, 511, F8, 56) (dual of [511, 363, 57]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {20,21,…,75}, and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(8154, 511, F8, 59) (dual of [511, 357, 60]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {17,18,…,75}, and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(8142, 511, F8, 54) (dual of [511, 369, 55]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {20,21,…,73}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
- Reed–Solomon code RS(6,8) [i]
- linear OA(81, 7, F8, 1) (dual of [7, 6, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(8157, 263, F8, 2, 59) (dual of [(263, 2), 369, 60]-NRT-code) | [i] | OOA Folding | |