Information on Result #701258
Linear OA(521, 68, F5, 9) (dual of [68, 47, 10]-code), using construction XX applied to C1 = C({1,4,6,8,11,17}), C2 = C({1,2,4,8,11,17}), C3 = C1 + C2 = C({1,4,8,11,17}), and C∩ = C1 ∩ C2 = C({1,2,4,6,8,11,17}) based on
- linear OA(518, 62, F5, 8) (dual of [62, 44, 9]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {1,4,6,8,11,17}, and minimum distance d ≥ |{5,8,11,…,26}|+1 = 9 (BCH-bound) [i]
- linear OA(518, 62, F5, 8) (dual of [62, 44, 9]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {1,2,4,8,11,17}, and minimum distance d ≥ |{2,5,8,…,23}|+1 = 9 (BCH-bound) [i]
- linear OA(521, 62, F5, 9) (dual of [62, 41, 10]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {1,2,4,6,8,11,17}, and minimum distance d ≥ |{2,5,8,…,26}|+1 = 10 (BCH-bound) [i]
- linear OA(515, 62, F5, 7) (dual of [62, 47, 8]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {1,4,8,11,17}, and minimum distance d ≥ |{5,8,11,…,23}|+1 = 8 (BCH-bound) [i]
- linear OA(50, 3, F5, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(50, 3, F5, 0) (dual of [3, 3, 1]-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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(521, 34, F5, 2, 9) (dual of [(34, 2), 47, 10]-NRT-code) | [i] | OOA Folding | |