Information on Result #893972
Linear OOA(786, 5764860, F7, 2, 10) (dual of [(5764860, 2), 11529634, 11]-NRT-code), using trace code based on linear OOA(4943, 2882430, F49, 2, 10) (dual of [(2882430, 2), 5764817, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4943, 5764860, F49, 10) (dual of [5764860, 5764817, 11]-code), using
- (u, u+v)-construction [i] 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(4938, 5764810, F49, 10) (dual of [5764810, 5764772, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(4937, 5764801, F49, 10) (dual of [5764801, 5764764, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(495, 50, F49, 5) (dual of [50, 45, 6]-code or 50-arc in PG(4,49)), using
- (u, u+v)-construction [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
None.