Information on Result #701260
Linear OA(530, 68, F5, 13) (dual of [68, 38, 14]-code), using construction XX applied to C1 = C({2,3,8,9,11,12,16,17,19}), C2 = C({2,3,7,8,9,11,12,16,17}), C3 = C1 + C2 = C({2,3,8,9,11,12,16,17}), and C∩ = C1 ∩ C2 = C({2,3,7,8,9,11,12,16,17,19}) based on
- linear OA(527, 62, F5, 12) (dual of [62, 35, 13]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {2,3,8,9,11,12,16,17,19}, and minimum distance d ≥ |{8,9,…,19}|+1 = 13 (BCH-bound) [i]
- linear OA(527, 62, F5, 12) (dual of [62, 35, 13]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {2,3,7,8,9,11,12,16,17}, and minimum distance d ≥ |{7,8,…,18}|+1 = 13 (BCH-bound) [i]
- linear OA(530, 62, F5, 13) (dual of [62, 32, 14]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {2,3,7,8,9,11,12,16,17,19}, and minimum distance d ≥ |{7,8,…,19}|+1 = 14 (BCH-bound) [i]
- linear OA(524, 62, F5, 11) (dual of [62, 38, 12]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {2,3,8,9,11,12,16,17}, and minimum distance d ≥ |{8,9,…,18}|+1 = 12 (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(530, 34, F5, 2, 13) (dual of [(34, 2), 38, 14]-NRT-code) | [i] | OOA Folding | |