Information on Result #700926
Linear OA(359, 136, F3, 18) (dual of [136, 77, 19]-code), using construction XX applied to C1 = C({1,10,16,19,22,25,26,31,34}), C2 = C({1,8,10,13,16,19,22,25,26,31}), C3 = C1 + C2 = C({1,10,16,19,22,25,26,31}), and C∩ = C1 ∩ C2 = C({1,8,10,13,16,19,22,25,26,31,34}) based on
- linear OA(345, 121, F3, 14) (dual of [121, 76, 15]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,10,16,19,22,25,26,31,34}, and minimum distance d ≥ |{−50,−30,−10,…,−32}|+1 = 15 (BCH-bound) [i]
- linear OA(350, 121, F3, 17) (dual of [121, 71, 18]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,8,10,13,16,19,22,25,26,31}, and minimum distance d ≥ |{−30,−10,10,…,48}|+1 = 18 (BCH-bound) [i]
- linear OA(355, 121, F3, 18) (dual of [121, 66, 19]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,8,10,13,16,19,22,25,26,31,34}, and minimum distance d ≥ |{−50,−30,−10,…,48}|+1 = 19 (BCH-bound) [i]
- linear OA(340, 121, F3, 13) (dual of [121, 81, 14]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,10,16,19,22,25,26,31}, and minimum distance d ≥ |{−30,−10,10,…,−32}|+1 = 14 (BCH-bound) [i]
- linear OA(30, 5, F3, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(34, 10, F3, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
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(359, 68, F3, 2, 18) (dual of [(68, 2), 77, 19]-NRT-code) | [i] | OOA Folding | |