MinT - Information on Result #2307969

Information on Result #2307969

OA(32⁵⁷, 324, S₃₂, 32), using 1 times code embedding in larger space based on OA(32⁵⁶, 323, S₃₂, 32), using

discarding parts of the base [i] based on linear OA(256³⁵, 323, F₂₅₆, 32) (dual of [323, 288, 33]-code), using
- constructionÂ X applied to AG(F,287P) âŠ‚ AG(F,289P) [i] based on
  1. linear OA(256³⁴, 320, F₂₅₆, 32) (dual of [320, 286, 33]-code), using algebraic-geometric code AG(F,287P) [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(256³², 320, F₂₅₆, 30) (dual of [320, 288, 31]-code), using algebraic-geometric code AG(F,289P) [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.