Information on Result #716632
Linear OA(8164, 566, F8, 55) (dual of [566, 402, 56]-code), using construction XX applied to C1 = C([503,41]), C2 = C([0,46]), C3 = C1 + C2 = C([0,41]), and C∩ = C1 ∩ C2 = C([503,46]) based on
- linear OA(8130, 511, F8, 50) (dual of [511, 381, 51]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−8,−7,…,41}, and designed minimum distance d ≥ |I|+1 = 51 [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(8145, 511, F8, 55) (dual of [511, 366, 56]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−8,−7,…,46}, and designed minimum distance d ≥ |I|+1 = 56 [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(813, 34, F8, 7) (dual of [34, 21, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using
- linear OA(86, 21, F8, 4) (dual of [21, 15, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-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(8164, 283, F8, 2, 55) (dual of [(283, 2), 402, 56]-NRT-code) | [i] | OOA Folding | |