Information on Result #2282146
Linear OA(8148, 556, F8, 51) (dual of [556, 408, 52]-code), using 1 times code embedding in larger space based on linear OA(8147, 555, F8, 51) (dual of [555, 408, 52]-code), using
- construction XX applied to C1 = C([37,81]), C2 = C([31,75]), C3 = C1 + C2 = C([37,75]), and C∩ = C1 ∩ C2 = C([31,81]) [i] based on
- linear OA(8118, 511, F8, 45) (dual of [511, 393, 46]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {37,38,…,81}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(8118, 511, F8, 45) (dual of [511, 393, 46]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {31,32,…,75}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(8133, 511, F8, 51) (dual of [511, 378, 52]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {31,32,…,81}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(8103, 511, F8, 39) (dual of [511, 408, 40]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {37,38,…,75}, and designed minimum distance d ≥ |I|+1 = 40 [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(8148, 278, F8, 2, 51) (dual of [(278, 2), 408, 52]-NRT-code) | [i] | OOA Folding | |