Information on Result #716735
Linear OA(8159, 558, F8, 55) (dual of [558, 399, 56]-code), using construction XX applied to C1 = C([505,42]), C2 = C([0,48]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([505,48]) based on
- linear OA(8130, 511, F8, 49) (dual of [511, 381, 50]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−6,−5,…,42}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(8127, 511, F8, 49) (dual of [511, 384, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [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 = {−6,−5,…,48}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(8112, 511, F8, 43) (dual of [511, 399, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [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(87, 22, F8, 5) (dual of [22, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code) (see above)
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 OA(8160, 559, F8, 55) (dual of [559, 399, 56]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8159, 279, F8, 2, 55) (dual of [(279, 2), 399, 56]-NRT-code) | [i] | OOA Folding | |