Information on Result #638136
Linear OA(5134, 156, F5, 79) (dual of [156, 22, 80]-code), using concatenation of two codes based on
- linear OA(2515, 26, F25, 15) (dual of [26, 11, 16]-code or 26-arc in PG(14,25)), using
- extended Reed–Solomon code RSe(11,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- algebraic-geometric code AG(F,5P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F, Q+2P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(54, 6, F5, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,5)), using
- extended Reed–Solomon code RSe(2,5) [i]
- Simplex code S(2,5) [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(5135, 157, F5, 79) (dual of [157, 22, 80]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5133, 155, F5, 78) (dual of [155, 22, 79]-code) | [i] | Truncation | |
| 3 | Linear OA(5132, 154, F5, 77) (dual of [154, 22, 78]-code) | [i] | ||
| 4 | Linear OA(5131, 153, F5, 76) (dual of [153, 22, 77]-code) | [i] | ||
| 5 | Linear OOA(5134, 78, F5, 2, 79) (dual of [(78, 2), 22, 80]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5134, 52, F5, 3, 79) (dual of [(52, 3), 22, 80]-NRT-code) | [i] | ||