Information on Result #682336
Linear OA(5123, 390675, F5, 18) (dual of [390675, 390552, 19]-code), using construction X applied to Ce(17) ⊂ Ce(11) based on
- linear OA(5113, 390625, F5, 18) (dual of [390625, 390512, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(573, 390625, F5, 12) (dual of [390625, 390552, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(510, 50, F5, 5) (dual of [50, 40, 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 OA(5124, 390676, F5, 18) (dual of [390676, 390552, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5124, 390677, F5, 18) (dual of [390677, 390553, 19]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(5123, 195337, F5, 2, 18) (dual of [(195337, 2), 390551, 19]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(5123, 130225, F5, 3, 18) (dual of [(130225, 3), 390552, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(5123, 43408, F5, 18, 18) (dual of [(43408, 18), 781221, 19]-NRT-code) | [i] | OA Folding and Stacking | |