Information on Result #686112
Linear OA(742, 67, F7, 24) (dual of [67, 25, 25]-code), using construction X applied to Ce(23) ⊂ Ce(15) based on
- linear OA(733, 49, F7, 24) (dual of [49, 16, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(724, 49, F7, 16) (dual of [49, 25, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(79, 18, F7, 7) (dual of [18, 9, 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), using
- extended quadratic residue code Qe(20,7) [i]
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- 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 OA(742, 67, F7, 23) (dual of [67, 25, 24]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(741, 66, F7, 23) (dual of [66, 25, 24]-code) | [i] | Truncation | |
| 3 | Linear OOA(742, 33, F7, 2, 24) (dual of [(33, 2), 24, 25]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(742, 22, F7, 3, 24) (dual of [(22, 3), 24, 25]-NRT-code) | [i] | ||