Information on Result #701115
Linear OA(445, 72, F4, 24) (dual of [72, 27, 25]-code), using construction X applied to C({1,3,5,7,9,11,13,22}) ⊂ C({1,3,5,7,9,11,13}) based on
- linear OA(444, 65, F4, 24) (dual of [65, 21, 25]-code), using the cyclic code C(A) with length 65 | 46−1, defining set A = {1,3,5,7,9,11,13,22}, and minimum distance d ≥ |{−23,−21,−19,…,23}|+1 = 25 (BCH-bound) [i]
- linear OA(438, 65, F4, 22) (dual of [65, 27, 23]-code), using the cyclic code C(A) with length 65 | 46−1, defining set A = {1,3,5,7,9,11,13}, and minimum distance d ≥ |{−21,−19,−17,…,21}|+1 = 23 (BCH-bound) [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 OA(451, 82, F4, 24) (dual of [82, 31, 25]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(449, 77, F4, 24) (dual of [77, 28, 25]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OA(450, 79, F4, 24) (dual of [79, 29, 25]-code) | [i] | ||
| 4 | Linear OA(451, 81, F4, 24) (dual of [81, 30, 25]-code) | [i] | ||
| 5 | Linear OOA(445, 36, F4, 2, 24) (dual of [(36, 2), 27, 25]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(445, 24, F4, 3, 24) (dual of [(24, 3), 27, 25]-NRT-code) | [i] | ||