Information on Result #683727
Linear OA(5138, 655, F5, 41) (dual of [655, 517, 42]-code), using construction XX applied to Ce(40) ⊂ Ce(35) ⊂ Ce(33) based on
- linear OA(5127, 625, F5, 41) (dual of [625, 498, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(5111, 625, F5, 36) (dual of [625, 514, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(5107, 625, F5, 34) (dual of [625, 518, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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.