Information on Result #686079
Linear OA(733, 57, F7, 20) (dual of [57, 24, 21]-code), using construction X applied to Ce(19) ⊂ Ce(16) based on
- linear OA(731, 49, F7, 20) (dual of [49, 18, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(725, 49, F7, 17) (dual of [49, 24, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using
- extended Reed–Solomon code RSe(6,7) [i]
- Hamming code H(2,7) [i]
- algebraic-geometric code AG(F, Q+1P) 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(736, 64, F7, 20) (dual of [64, 28, 21]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(737, 69, F7, 20) (dual of [69, 32, 21]-code) | [i] | ||
| 3 | Linear OA(738, 75, F7, 20) (dual of [75, 37, 21]-code) | [i] | ||
| 4 | Linear OOA(733, 28, F7, 2, 20) (dual of [(28, 2), 23, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(733, 19, F7, 3, 20) (dual of [(19, 3), 24, 21]-NRT-code) | [i] | ||