Information on Result #732943
Linear OA(2553, 390663, F25, 12) (dual of [390663, 390610, 13]-code), using (u, u+v)-construction based on
- linear OA(257, 29, F25, 6) (dual of [29, 22, 7]-code), using
- construction X applied to AG(F, Q+8P) ⊂ AG(F, Q+9P) [i] based on
- linear OA(256, 26, F25, 6) (dual of [26, 20, 7]-code or 26-arc in PG(5,25)), using algebraic-geometric code AG(F, Q+8P) 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]
- linear OA(254, 26, F25, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using 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 (see above)
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F, Q+8P) ⊂ AG(F, Q+9P) [i] based on
- linear OA(2546, 390634, F25, 12) (dual of [390634, 390588, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(2545, 390625, F25, 12) (dual of [390625, 390580, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2537, 390625, F25, 10) (dual of [390625, 390588, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(251, 9, F25, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
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.