MinT - Information on Result #2501216

Information on Result #2501216

Linear OOA(4²⁵³, 456, F₄, 2, 82) (dual of [(456, 2), 659, 83]-NRT-code), using 4¹ times duplication based on linear OOA(4²⁵², 456, F₄, 2, 82) (dual of [(456, 2), 660, 83]-NRT-code), using

trace code [i] based on linear OOA(16¹²⁶, 228, F₁₆, 2, 82) (dual of [(228, 2), 330, 83]-NRT-code), using
- constructionÂ X applied to AG(2;F,365P) âŠ‚ AG(2;F,370P) [i] based on
  1. linear OOA(16¹²², 224, F₁₆, 2, 82) (dual of [(224, 2), 326, 83]-NRT-code), using algebraic-geometric NRT-code AG(2;F,365P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(16¹¹⁷, 224, F₁₆, 2, 77) (dual of [(224, 2), 331, 78]-NRT-code), using algebraic-geometric NRT-code AG(2;F,370P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225 (see above)
  3. linear OOA(16⁴, 4, F₁₆, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁴, 16, F₁₆, 2, 4) (dual of [(16, 2), 28, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;28,16) [i]

Mode: Constructive and 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.