Information on Result #712513
Linear OA(765, 78, F7, 41) (dual of [78, 13, 42]-code), using construction XX applied to C1 = C([8,40]), C2 = C([0,31]), C3 = C1 + C2 = C([8,31]), and C∩ = C1 ∩ C2 = C([0,40]) based on
- linear OA(741, 48, F7, 33) (dual of [48, 7, 34]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {8,9,…,40}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(746, 48, F7, 41) (dual of [48, 2, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {8,9,…,31}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(710, 16, F7, 8) (dual of [16, 6, 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(79, 14, F7, 7) (dual of [14, 5, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(79, 19, F7, 7) (dual of [19, 10, 8]-code), using
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code) (see above)
- discarding factors / shortening the dual code based on linear OA(79, 19, F7, 7) (dual of [19, 10, 8]-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 OOA(765, 39, F7, 2, 41) (dual of [(39, 2), 13, 42]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(765, 26, F7, 3, 41) (dual of [(26, 3), 13, 42]-NRT-code) | [i] | ||