MinT - Information on Result #1297033

Information on Result #1297033

Linear OA(16¹¹⁸, 646, F₁₆, 56) (dual of [646, 528, 57]-code), using trace code based on linear OA(256⁵⁹, 323, F₂₅₆, 56) (dual of [323, 264, 57]-code), using

constructionÂ X applied to AG(F,263P) âŠ‚ AG(F,265P) [i] based on
1. linear OA(256⁵⁸, 320, F₂₅₆, 56) (dual of [320, 262, 57]-code), using algebraic-geometric code AG(F,263P) [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(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 (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.