Information on Result #686061
Linear OA(737, 57, F7, 24) (dual of [57, 20, 25]-code), using construction X applied to Ce(23) ⊂ Ce(18) 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(729, 49, F7, 19) (dual of [49, 20, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(74, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using
- extended Reed–Solomon code RSe(4,7) [i]
- algebraic-geometric code AG(F, Q+0P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [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(738, 58, F7, 24) (dual of [58, 20, 25]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(736, 56, F7, 23) (dual of [56, 20, 24]-code) | [i] | Truncation | |
| 3 | Linear OA(735, 55, F7, 22) (dual of [55, 20, 23]-code) | [i] | ||
| 4 | Linear OOA(737, 28, F7, 2, 24) (dual of [(28, 2), 19, 25]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(737, 19, F7, 3, 24) (dual of [(19, 3), 20, 25]-NRT-code) | [i] | ||