Information on Result #712112
Linear OA(5147, 680, F5, 41) (dual of [680, 533, 42]-code), using construction XX applied to C1 = C([131,166]), C2 = C([126,158]), C3 = C1 + C2 = C([131,158]), 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(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(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(589, 624, F5, 28) (dual of [624, 535, 29]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {131,132,…,158}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(514, 36, F5, 7) (dual of [36, 22, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(514, 52, F5, 7) (dual of [52, 38, 8]-code), using
- trace code [i] based on linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
- extended Reed–Solomon code RSe(19,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- algebraic-geometric code AG(F,9P) with 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,6P) with 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(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(514, 52, F5, 7) (dual of [52, 38, 8]-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.