Information on Result #712055
Linear OA(5149, 681, F5, 41) (dual of [681, 532, 42]-code), using construction XX applied to C1 = C([131,166]), C2 = C([126,157]), C3 = C1 + C2 = C([131,157]), and C∩ = C1 ∩ C2 = C([126,166]) based on
- linear OA(5113, 624, F5, 36) (dual of [624, 511, 37]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {131,132,…,166}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(599, 624, F5, 32) (dual of [624, 525, 33]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {126,127,…,157}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(5127, 624, F5, 41) (dual of [624, 497, 42]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {126,127,…,166}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(585, 624, F5, 27) (dual of [624, 539, 28]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {131,132,…,157}, 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(56, 20, F5, 4) (dual of [20, 14, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), 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.