Information on Result #716597
Linear OA(8154, 556, F8, 53) (dual of [556, 402, 54]-code), using construction XX applied to C1 = C([33,81]), C2 = C([29,74]), C3 = C1 + C2 = C([33,74]), and C∩ = C1 ∩ C2 = C([29,81]) based on
- linear OA(8127, 511, F8, 49) (dual of [511, 384, 50]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {33,34,…,81}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(8121, 511, F8, 46) (dual of [511, 390, 47]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {29,30,…,74}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(8139, 511, F8, 53) (dual of [511, 372, 54]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {29,30,…,81}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(8109, 511, F8, 42) (dual of [511, 402, 43]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {33,34,…,74}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(811, 29, F8, 6) (dual of [29, 18, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- linear OA(84, 16, F8, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,8)), 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(8154, 278, F8, 2, 53) (dual of [(278, 2), 402, 54]-NRT-code) | [i] | OOA Folding | |