MinT - Information on Result #671657

Information on Result #671657

Linear OA(256⁵⁷, 522, F₂₅₆, 36) (dual of [522, 465, 37]-code), using (u,Â u+v)-construction based on

linear OA(256¹⁹, 260, F₂₅₆, 18) (dual of [260, 241, 19]-code), using
- constructionÂ X applied to AG(F,119P) âŠ‚ AG(F,120P) [i] based on
  1. linear OA(256¹⁸, 257, F₂₅₆, 18) (dual of [257, 239, 19]-code or 257-arc in PG(17,256)), using algebraic-geometric code AG(F,119P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
  2. linear OA(256¹⁶, 257, F₂₅₆, 16) (dual of [257, 241, 17]-code or 257-arc in PG(15,256)), using algebraic-geometric code AG(F,120P) with degPÂ =Â 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), using
    - discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(256³⁸, 262, F₂₅₆, 36) (dual of [262, 224, 37]-code), using
- constructionÂ X applied to AG(F, Q+72P) âŠ‚ AG(F, Q+73P) [i] based on
  1. linear OA(256³⁶, 257, F₂₅₆, 36) (dual of [257, 221, 37]-code or 257-arc in PG(35,256)), using algebraic-geometric code AG(F,110P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  2. linear OA(256³³, 257, F₂₅₆, 33) (dual of [257, 224, 34]-code or 257-arc in PG(32,256)), using algebraic-geometric code AG(F, Q+110P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  3. linear OA(256², 5, F₂₅₆, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,256)), using
    - discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
      - Reedâ€“Solomon code RS(254,256) [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.