Information on Result #700929
Linear OA(372, 138, F3, 24) (dual of [138, 66, 25]-code), using construction XX applied to C1 = C({1,4,7,8,10,13,16,19,20,22,25,26,67}), C2 = C({1,4,7,8,10,13,16,19,22,25,26,31}), C3 = C1 + C2 = C({1,4,7,8,10,13,16,19,22,25,26}), and C∩ = C1 ∩ C2 = C({1,4,7,8,10,13,16,19,20,22,25,26,31,67}) based on
- linear OA(365, 121, F3, 23) (dual of [121, 56, 24]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,4,7,8,10,13,16,19,20,22,25,26,67}, and minimum distance d ≥ |{10,30,50,…,−34}|+1 = 24 (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(370, 121, F3, 25) (dual of [121, 51, 26]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,4,7,8,10,13,16,19,20,22,25,26,31,67}, and minimum distance d ≥ |{−30,−10,10,…,−34}|+1 = 26 (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(31, 11, F3, 1) (dual of [11, 10, 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(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 (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(372, 69, F3, 2, 24) (dual of [(69, 2), 66, 25]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(372, 46, F3, 3, 24) (dual of [(46, 3), 66, 25]-NRT-code) | [i] | ||