Information on Result #671574

Linear OA(25654, 66057, F256, 19) (dual of [66057, 66003, 20]-code), using (u, u−v, u+v+w)-construction based on
  1. linear OA(2567, 260, F256, 6) (dual of [260, 253, 7]-code), using
  2. linear OA(25610, 260, F256, 9) (dual of [260, 250, 10]-code), using
    • construction X applied to AG(F, Q+122P) ⊂ AG(F, Q+123P) [i] based on
      1. linear OA(2569, 257, F256, 9) (dual of [257, 248, 10]-code or 257-arc in PG(8,256)), using algebraic-geometric code AG(F, Q+122P) with degQ = 3 and degP = 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
      2. linear OA(2567, 257, F256, 7) (dual of [257, 250, 8]-code or 257-arc in PG(6,256)), using algebraic-geometric code AG(F, Q+123P) with degQ = 3 and degP = 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
      3. linear OA(2561, 3, F256, 1) (dual of [3, 2, 2]-code) (see above)
  3. linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using
    • the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]

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.