Information on Result #711514
Linear OA(5120, 670, F5, 33) (dual of [670, 550, 34]-code), using construction XX applied to C1 = C([126,156]), C2 = C([135,158]), C3 = C1 + C2 = C([135,156]), and C∩ = C1 ∩ C2 = C([126,158]) based on
- linear OA(595, 624, F5, 31) (dual of [624, 529, 32]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {126,127,…,156}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(577, 624, F5, 24) (dual of [624, 547, 25]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {135,136,…,158}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(5103, 624, F5, 33) (dual of [624, 521, 34]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {126,127,…,158}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(569, 624, F5, 22) (dual of [624, 555, 23]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {135,136,…,156}, and designed minimum distance d ≥ |I|+1 = 23 [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(51, 9, F5, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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.