Information on Result #711986
Linear OA(5147, 678, F5, 40) (dual of [678, 531, 41]-code), using construction XX applied to C1 = C([120,155]), C2 = C([129,159]), C3 = C1 + C2 = C([129,155]), and C∩ = C1 ∩ C2 = C([120,159]) based on
- linear OA(5114, 624, F5, 36) (dual of [624, 510, 37]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {120,121,…,155}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(599, 624, F5, 31) (dual of [624, 525, 32]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {129,130,…,159}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(5127, 624, F5, 40) (dual of [624, 497, 41]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {120,121,…,159}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(586, 624, F5, 27) (dual of [624, 538, 28]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {129,130,…,155}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(516, 37, F5, 8) (dual of [37, 21, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(516, 52, F5, 8) (dual of [52, 36, 9]-code), using
- trace code [i] based on linear OA(258, 26, F25, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)), using
- extended Reed–Solomon code RSe(18,25) [i]
- algebraic-geometric code AG(F, Q+7P) with degQ = 3 and 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+5P) 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(258, 26, F25, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)), using
- discarding factors / shortening the dual code based on linear OA(516, 52, F5, 8) (dual of [52, 36, 9]-code), using
- linear OA(54, 17, F5, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,5)), 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
None.