Information on Result #682402
Linear OA(5137, 78164, F5, 23) (dual of [78164, 78027, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,8]) based on
- linear OA(5127, 78126, F5, 23) (dual of [78126, 77999, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(599, 78126, F5, 17) (dual of [78126, 78027, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(510, 38, F5, 5) (dual of [38, 28, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(510, 52, F5, 5) (dual of [52, 42, 6]-code), using
- trace code [i] based on linear OA(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
- extended Reed–Solomon code RSe(21,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- algebraic-geometric code AG(F,10P) 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+6P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- trace code [i] based on linear OA(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(510, 52, F5, 5) (dual of [52, 42, 6]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(5137, 72947, F5, 2, 23) (dual of [(72947, 2), 145757, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5137, 72947, F5, 3, 23) (dual of [(72947, 3), 218704, 24]-NRT-code) | [i] | ||
| 3 | Digital (114, 137, 72947)-net over F5 | [i] | ||