Information on Result #701280
Linear OA(540, 68, F5, 20) (dual of [68, 28, 21]-code), using construction XX applied to C1 = C({1,4,6,11,16,17,19,21,22,24,31,32,34}), C2 = C({1,3,4,6,11,16,17,19,21,22,24,31,32}), C3 = C1 + C2 = C({1,4,6,11,16,17,19,21,22,24,31,32}), and C∩ = C1 ∩ C2 = C({1,3,4,6,11,16,17,19,21,22,24,31,32,34}) based on
- linear OA(537, 62, F5, 19) (dual of [62, 25, 20]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {1,4,6,11,16,17,19,21,22,24,31,32,34}, and minimum distance d ≥ |{16,17,…,34}|+1 = 20 (BCH-bound) [i]
- linear OA(537, 62, F5, 19) (dual of [62, 25, 20]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {1,3,4,6,11,16,17,19,21,22,24,31,32}, and minimum distance d ≥ |{15,16,…,33}|+1 = 20 (BCH-bound) [i]
- linear OA(540, 62, F5, 20) (dual of [62, 22, 21]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {1,3,4,6,11,16,17,19,21,22,24,31,32,34}, and minimum distance d ≥ |{15,16,…,34}|+1 = 21 (BCH-bound) [i]
- linear OA(534, 62, F5, 18) (dual of [62, 28, 19]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {1,4,6,11,16,17,19,21,22,24,31,32}, and minimum distance d ≥ |{16,17,…,33}|+1 = 19 (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(540, 34, F5, 2, 20) (dual of [(34, 2), 28, 21]-NRT-code) | [i] | OOA Folding | |