Information on Result #2265659
Linear OA(365, 136, F3, 22) (dual of [136, 71, 23]-code), using 1 times code embedding in larger space based on linear OA(364, 135, F3, 22) (dual of [135, 71, 23]-code), using
- construction XX applied to C1 = C({1,7,8,10,13,16,19,22,25,26,31}), C2 = C({1,4,7,8,10,13,16,19,22,25,26}), C3 = C1 + C2 = C({1,7,8,10,13,16,19,22,25,26}), and C∩ = C1 ∩ C2 = C({1,4,7,8,10,13,16,19,22,25,26,31}) [i] based on
- linear OA(355, 121, F3, 19) (dual of [121, 66, 20]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,7,8,10,13,16,19,22,25,26,31}, and minimum distance d ≥ |{−30,−10,10,…,−33}|+1 = 20 (BCH-bound) [i]
- linear OA(355, 121, F3, 20) (dual of [121, 66, 21]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,4,7,8,10,13,16,19,22,25,26}, and minimum distance d ≥ |{10,30,50,…,27}|+1 = 21 (BCH-bound) [i]
- linear OA(360, 121, F3, 22) (dual of [121, 61, 23]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,4,7,8,10,13,16,19,22,25,26,31}, and minimum distance d ≥ |{−30,−10,10,…,27}|+1 = 23 (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 = {1,7,8,10,13,16,19,22,25,26}, and minimum distance d ≥ |{10,30,50,…,−33}|+1 = 18 (BCH-bound) [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(33, 8, F3, 2) (dual of [8, 5, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), 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(365, 68, F3, 2, 22) (dual of [(68, 2), 71, 23]-NRT-code) | [i] | OOA Folding | |