Information on Result #716415
Linear OA(8141, 558, F8, 48) (dual of [558, 417, 49]-code), using construction XX applied to C1 = C([505,35]), C2 = C([0,41]), C3 = C1 + C2 = C([0,35]), and C∩ = C1 ∩ C2 = C([505,41]) based on
- linear OA(8112, 511, F8, 42) (dual of [511, 399, 43]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−6,−5,…,35}, and designed minimum distance d ≥ |I|+1 = 43 [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(8127, 511, F8, 48) (dual of [511, 384, 49]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−6,−5,…,41}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(894, 511, F8, 36) (dual of [511, 417, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [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(8142, 559, F8, 48) (dual of [559, 417, 49]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8141, 279, F8, 2, 48) (dual of [(279, 2), 417, 49]-NRT-code) | [i] | OOA Folding | |