Information on Result #701584
Linear OA(869, 76, F8, 55) (dual of [76, 7, 56]-code), using construction X applied to C([1,42]) ⊂ C({1,2,3,4,5,6,7,9,11,12,13,14,17,18,25,26,27,33,34,35,36,42}) based on
- linear OA(869, 73, F8, 55) (dual of [73, 4, 56]-code), using the narrow-sense BCH-code C(I) with length 73 | 83−1, defining interval I = [1,42], and minimum distance d ≥ |{−9,12,33,…,30}|+1 = 56 (BCH-bound) [i]
- linear OA(866, 73, F8, 54) (dual of [73, 7, 55]-code), using the cyclic code C(A) with length 73 | 83−1, defining set A = {1,2,3,4,5,6,7,9,11,12,13,14,17,18,25,26,27,33,34,35,36,42}, and minimum distance d ≥ |{−9,12,33,…,9}|+1 = 55 (BCH-bound) [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-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 OOA(869, 38, F8, 2, 55) (dual of [(38, 2), 7, 56]-NRT-code) | [i] | OOA Folding | |