Information on Result #2281764
Linear OA(8109, 550, F8, 37) (dual of [550, 441, 38]-code), using 1 times code embedding in larger space based on linear OA(8108, 549, F8, 37) (dual of [549, 441, 38]-code), using
- construction XX applied to C1 = C([49,81]), C2 = C([45,75]), C3 = C1 + C2 = C([49,75]), and C∩ = C1 ∩ C2 = C([45,81]) [i] based on
- linear OA(885, 511, F8, 33) (dual of [511, 426, 34]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {49,50,…,81}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(882, 511, F8, 31) (dual of [511, 429, 32]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {45,46,…,75}, and designed minimum distance d ≥ |I|+1 = 32 [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 = {45,46,…,81}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(870, 511, F8, 27) (dual of [511, 441, 28]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {49,50,…,75}, and designed minimum distance d ≥ |I|+1 = 28 [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(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(8109, 275, F8, 2, 37) (dual of [(275, 2), 441, 38]-NRT-code) | [i] | OOA Folding | |