Information on Result #686030
Linear OA(765, 74, F7, 46) (dual of [74, 9, 47]-code), using construction X applied to C([0,24]) ⊂ C([0,16]) based on
- linear OA(749, 50, F7, 49) (dual of [50, 1, 50]-code or 50-arc in PG(48,7)), using the expurgated narrow-sense BCH-code C(I) with length 50 | 74−1, defining interval I = [0,24], and minimum distance d ≥ |{−14,−3,8,…,14}|+1 = 50 (BCH-bound) [i]
- linear OA(741, 50, F7, 33) (dual of [50, 9, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 50 | 74−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(716, 24, F7, 12) (dual of [24, 8, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(716, 32, F7, 12) (dual of [32, 16, 13]-code), using
- extended quadratic residue code Qe(32,7) [i]
- discarding factors / shortening the dual code based on linear OA(716, 32, F7, 12) (dual of [32, 16, 13]-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 OA(762, 71, F7, 43) (dual of [71, 9, 44]-code) | [i] | Truncation | |
| 2 | Linear OOA(765, 37, F7, 2, 46) (dual of [(37, 2), 9, 47]-NRT-code) | [i] | OOA Folding | |