MinT - Information on Result #1845730

Information on Result #1845730

OA(64⁵⁹, 323, S₆₄, 41), using discarding parts of the base based on linear OA(256⁴⁴, 323, F₂₅₆, 41) (dual of [323, 279, 42]-code), using

constructionÂ X applied to AG(F,278P) âŠ‚ AG(F,280P) [i] based on
1. linear OA(256⁴³, 320, F₂₅₆, 41) (dual of [320, 277, 42]-code), using algebraic-geometric code AG(F,278P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
  - sharp bound on the number of rational points on curves with genus 2 [i]
2. linear OA(256⁴¹, 320, F₂₅₆, 39) (dual of [320, 279, 40]-code), using algebraic-geometric code AG(F,280P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321 (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]

Mode: Arbitrary.

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.