Information on Result #701303
Linear OA(749, 68, F7, 28) (dual of [68, 19, 29]-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([0,18]) 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(729, 48, F7, 19) (dual of [48, 19, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [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 OOA(749, 34, F7, 2, 28) (dual of [(34, 2), 19, 29]-NRT-code) | [i] | OOA Folding | |