MinT - Information on Result #2544336

Information on Result #2544336

OOA(128²⁶, 324, S₁₂₈, 2, 16), using 1 times NRT-code embedding in larger space based on OOA(128²⁴, 323, S₁₂₈, 2, 16), using

discarding parts of the base [i] based on linear OOA(256²¹, 323, F₂₅₆, 2, 16) (dual of [(323, 2), 625, 17]-NRT-code), using
- constructionÂ X applied to AG(2;F,623P) âŠ‚ AG(2;F,627P) [i] based on
  1. linear OOA(256¹⁸, 320, F₂₅₆, 2, 16) (dual of [(320, 2), 622, 17]-NRT-code), using algebraic-geometric NRT-code AG(2;F,623P) [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(256¹⁴, 320, F₂₅₆, 2, 12) (dual of [(320, 2), 626, 13]-NRT-code), using algebraic-geometric NRT-code AG(2;F,627P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321 (see above)
  3. linear OOA(256³, 3, F₂₅₆, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(256³, 256, F₂₅₆, 2, 3) (dual of [(256, 2), 509, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;509,256) [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.