Information on Result #716791
Linear OA(8157, 544, F8, 56) (dual of [544, 387, 57]-code), using construction XX applied to C1 = C([505,46]), C2 = C([0,49]), C3 = C1 + C2 = C([0,46]), and C∩ = C1 ∩ C2 = C([505,49]) based on
- linear OA(8142, 511, F8, 53) (dual of [511, 369, 54]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−6,−5,…,46}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(8130, 511, F8, 50) (dual of [511, 381, 51]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,49], and designed minimum distance d ≥ |I|+1 = 51 [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 = {−6,−5,…,49}, and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(8124, 511, F8, 47) (dual of [511, 387, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(87, 25, F8, 5) (dual of [25, 18, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- 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]
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, 272, F8, 2, 56) (dual of [(272, 2), 387, 57]-NRT-code) | [i] | OOA Folding | |