Information on Result #734623
Linear OA(4936, 117702, F49, 11) (dual of [117702, 117666, 12]-code), using (u, u+v)-construction based on
- linear OA(495, 50, F49, 5) (dual of [50, 45, 6]-code or 50-arc in PG(4,49)), using
- extended Reed–Solomon code RSe(45,49) [i]
- the expurgated narrow-sense BCH-code C(I) with length 50 | 492−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- algebraic-geometric code AG(F,22P) with degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using the rational function field F49(x) [i]
- algebraic-geometric code AG(F, Q+14P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- algebraic-geometric code AG(F, Q+8P) with degQ = 4 and degPÂ =Â 5 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(4931, 117652, F49, 11) (dual of [117652, 117621, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(4931, 117649, F49, 11) (dual of [117649, 117618, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(4928, 117649, F49, 10) (dual of [117649, 117621, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(490, 3, F49, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
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(4936, 117702, F49, 2, 11) (dual of [(117702, 2), 235368, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4936, 117702, F49, 3, 11) (dual of [(117702, 3), 353070, 12]-NRT-code) | [i] | ||
| 3 | Digital (25, 36, 117702)-net over F49 | [i] | ||
| 4 | Linear OOA(4936, 58851, F49, 2, 11) (dual of [(58851, 2), 117666, 12]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4936, 39234, F49, 3, 11) (dual of [(39234, 3), 117666, 12]-NRT-code) | [i] | ||
| 6 | Linear OOA(4936, 23540, F49, 11, 11) (dual of [(23540, 11), 258904, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |