Information on Result #685923
Linear OA(752, 68, F7, 33) (dual of [68, 16, 34]-code), using construction XX applied to C([0,65]) ⊂ C([0,47]) ⊂ C([1,47]) based on
- linear OA(741, 48, F7, 33) (dual of [48, 7, 34]-code), using contraction [i] based on linear OA(789, 96, F7, 67) (dual of [96, 7, 68]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,65], and minimum distance d ≥ |{−1,0,…,65}|+1 = 68 (BCH-bound) [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using contraction [i] based on linear OA(781, 96, F7, 49) (dual of [96, 15, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,47], and minimum distance d ≥ |{−1,0,…,47}|+1 = 50 (BCH-bound) [i]
- linear OA(732, 48, F7, 23) (dual of [48, 16, 24]-code), using contraction [i] based on linear OA(780, 96, F7, 47) (dual of [96, 16, 48]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(710, 19, F7, 8) (dual of [19, 9, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(752, 68, F7, 32) (dual of [68, 16, 33]-code) | [i] | Strength Reduction | |
| 2 | Linear OOA(752, 34, F7, 2, 33) (dual of [(34, 2), 16, 34]-NRT-code) | [i] | OOA Folding | |