Information on Result #716211
Linear OA(8121, 542, F8, 43) (dual of [542, 421, 44]-code), using construction XX applied to C1 = C([33,72]), C2 = C([39,75]), C3 = C1 + C2 = C([39,72]), and C∩ = C1 ∩ C2 = C([33,75]) based on
- linear OA(8105, 511, F8, 40) (dual of [511, 406, 41]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {33,34,…,72}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(897, 511, F8, 37) (dual of [511, 414, 38]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {39,40,…,75}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8112, 511, F8, 43) (dual of [511, 399, 44]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {33,34,…,75}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(890, 511, F8, 34) (dual of [511, 421, 35]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {39,40,…,72}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- 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), using
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [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 OA(8122, 543, F8, 43) (dual of [543, 421, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8121, 271, F8, 2, 43) (dual of [(271, 2), 421, 44]-NRT-code) | [i] | OOA Folding | |