MinT - Information on Result #659567

Information on Result #659567

Linear OA(4²²⁸, 1064, F₄, 53) (dual of [1064, 836, 54]-code), using trace code based on linear OA(256⁵⁷, 266, F₂₅₆, 53) (dual of [266, 209, 54]-code), using

constructionÂ X applied to AG(F, Q+40P) âŠ‚ AG(F, Q+41P) [i] based on
1. linear OA(256⁵³, 257, F₂₅₆, 53) (dual of [257, 204, 54]-code or 257-arc in PG(52,256)), using algebraic-geometric code AG(F, Q+100P) with degQ = 3 and 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(256⁴⁸, 257, F₂₅₆, 48) (dual of [257, 209, 49]-code or 257-arc in PG(47,256)), using algebraic-geometric code AG(F,104P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
3. linear OA(256⁴, 9, F₂₅₆, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,256)), using
  - discarding factors / shortening the dual code based on linear OA(256⁴, 256, F₂₅₆, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
    - Reedâ€“Solomon code RS(252,256) [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.