Information on Result #716502
Linear OA(8127, 527, F8, 47) (dual of [527, 400, 48]-code), using construction XX applied to C1 = C([508,41]), C2 = C([0,43]), C3 = C1 + C2 = C([0,41]), and C∩ = C1 ∩ C2 = C([508,43]) based on
- linear OA(8118, 511, F8, 45) (dual of [511, 393, 46]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−3,−2,…,41}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(8115, 511, F8, 44) (dual of [511, 396, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(8124, 511, F8, 47) (dual of [511, 387, 48]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−3,−2,…,43}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(8109, 511, F8, 42) (dual of [511, 402, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [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(8127, 263, F8, 2, 47) (dual of [(263, 2), 399, 48]-NRT-code) | [i] | OOA Folding | |