Information on Result #701296
Linear OA(755, 78, F7, 30) (dual of [78, 23, 31]-code), using construction X applied to C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,27,34,41}) ⊂ C([0,16]) based on
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,27,34,41}, and minimum distance d ≥ |{−7,−6,…,23}|+1 = 32 (BCH-bound) [i]
- linear OA(725, 48, F7, 17) (dual of [48, 23, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(716, 30, F7, 12) (dual of [30, 14, 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 OOA(755, 39, F7, 2, 30) (dual of [(39, 2), 23, 31]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(755, 26, F7, 3, 30) (dual of [(26, 3), 23, 31]-NRT-code) | [i] | ||