MinT - Information on Result #2544355

Information on Result #2544355

OOA(128³⁴, 325, S₁₂₈, 2, 22), using 1 times NRT-code embedding in larger space based on OOA(128³², 324, S₁₂₈, 2, 22), using

discarding parts of the base [i] based on linear OOA(256²⁸, 324, F₂₅₆, 2, 22) (dual of [(324, 2), 620, 23]-NRT-code), using
- constructionÂ X applied to AG(2;F,617P) âŠ‚ AG(2;F,622P) [i] based on
  1. linear OOA(256²⁴, 320, F₂₅₆, 2, 22) (dual of [(320, 2), 616, 23]-NRT-code), using algebraic-geometric NRT-code AG(2;F,617P) [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 OOA(256¹⁹, 320, F₂₅₆, 2, 17) (dual of [(320, 2), 621, 18]-NRT-code), using algebraic-geometric NRT-code AG(2;F,622P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321 (see above)
  3. linear OOA(256⁴, 4, F₂₅₆, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(256⁴, 256, F₂₅₆, 2, 4) (dual of [(256, 2), 508, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;508,256) [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.