Information on Result #683371
Linear OA(5116, 656, F5, 32) (dual of [656, 540, 33]-code), using construction XX applied to C([0,16]) ⊂ C([0,13]) ⊂ C([0,12]) based on
- linear OA(5105, 626, F5, 33) (dual of [626, 521, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 58−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(589, 626, F5, 27) (dual of [626, 537, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 58−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(581, 626, F5, 25) (dual of [626, 545, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 58−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(57, 26, F5, 4) (dual of [26, 19, 5]-code), using
- base reduction for projective spaces (embedding PG(3,25) in PG(6,5)) [i] based on linear OA(254, 26, F25, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using
- extended Reed–Solomon code RSe(22,25) [i]
- algebraic-geometric code AG(F, Q+9P) 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,7P) with degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- base reduction for projective spaces (embedding PG(3,25) in PG(6,5)) [i] based on linear OA(254, 26, F25, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using
- linear OA(51, 4, F5, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-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.