Information on Result #2281915
Linear OA(8124, 556, F8, 42) (dual of [556, 432, 43]-code), using 1 times code embedding in larger space based on linear OA(8123, 555, F8, 42) (dual of [555, 432, 43]-code), using
- construction XX applied to C1 = C([46,81]), C2 = C([40,75]), C3 = C1 + C2 = C([46,75]), and C∩ = C1 ∩ C2 = C([40,81]) [i] based on
- linear OA(894, 511, F8, 36) (dual of [511, 417, 37]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {46,47,…,81}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(894, 511, F8, 36) (dual of [511, 417, 37]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {40,41,…,75}, and designed minimum distance d ≥ |I|+1 = 37 [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 = {40,41,…,81}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(879, 511, F8, 30) (dual of [511, 432, 31]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {46,47,…,75}, and designed minimum distance d ≥ |I|+1 = 31 [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(87, 22, F8, 5) (dual of [22, 15, 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 OOA(8124, 278, F8, 2, 42) (dual of [(278, 2), 432, 43]-NRT-code) | [i] | OOA Folding | |