Information on Result #734495
Linear OA(4952, 2460, F49, 20) (dual of [2460, 2408, 21]-code), using (u, u+v)-construction based on
- linear OA(4913, 57, F49, 10) (dual of [57, 44, 11]-code), using
- construction X applied to AG(F, Q+18P) ⊂ AG(F, Q+20P) [i] based on
- linear OA(4910, 50, F49, 10) (dual of [50, 40, 11]-code or 50-arc in PG(9,49)), using algebraic-geometric code AG(F, Q+18P) with degQ = 3 and 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]
- linear OA(496, 50, F49, 6) (dual of [50, 44, 7]-code or 50-arc in PG(5,49)), using algebraic-geometric code AG(F, Q+20P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(493, 7, F49, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,49) or 7-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- construction X applied to AG(F, Q+18P) ⊂ AG(F, Q+20P) [i] based on
- linear OA(4939, 2403, F49, 20) (dual of [2403, 2364, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(4939, 2401, F49, 20) (dual of [2401, 2362, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(4937, 2401, F49, 19) (dual of [2401, 2364, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 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(19) ⊂ Ce(18) [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(4952, 820, F49, 3, 20) (dual of [(820, 3), 2408, 21]-NRT-code) | [i] | OOA Folding | |