MinT - Information on Result #2307679

Information on Result #2307679

Linear OA(16¹¹⁵, 647, F₁₆, 54) (dual of [647, 532, 55]-code), using 1 times code embedding in larger space based on linear OA(16¹¹⁴, 646, F₁₆, 54) (dual of [646, 532, 55]-code), using

trace code [i] based on linear OA(256⁵⁷, 323, F₂₅₆, 54) (dual of [323, 266, 55]-code), using
- constructionÂ X applied to AG(F,265P) âŠ‚ AG(F,267P) [i] based on
  1. linear OA(256⁵⁶, 320, F₂₅₆, 54) (dual of [320, 264, 55]-code), using algebraic-geometric code AG(F,265P) [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(256⁵⁴, 320, F₂₅₆, 52) (dual of [320, 266, 53]-code), using algebraic-geometric code AG(F,267P) [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: 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.