Information on Result #701597
Linear OA(914, 44, F9, 8) (dual of [44, 30, 9]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,31}), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,31}) based on
- linear OA(912, 40, F9, 7) (dual of [40, 28, 8]-code), using the cyclic code C(A) with length 40 | 92−1, defining set A = {0,1,2,3,4,5,31}, and minimum distance d ≥ |{−1,0,…,5}|+1 = 8 (BCH-bound) [i]
- linear OA(912, 40, F9, 7) (dual of [40, 28, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 40 | 92−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(914, 40, F9, 8) (dual of [40, 26, 9]-code), using the cyclic code C(A) with length 40 | 92−1, defining set A = {0,1,2,3,4,5,6,31}, and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]
- linear OA(910, 40, F9, 6) (dual of [40, 30, 7]-code), using the expurgated narrow-sense BCH-code C(I) with length 40 | 92−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(90, 2, F9, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(90, 2, F9, 0) (dual of [2, 2, 1]-code) (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 OA(9147, 6605, F9, 38) (dual of [6605, 6458, 39]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 2 | Linear OA(9143, 6605, F9, 37) (dual of [6605, 6462, 38]-code) | [i] | ||
| 3 | Linear OOA(914, 22, F9, 2, 8) (dual of [(22, 2), 30, 9]-NRT-code) | [i] | OOA Folding | |