MinT - Information on Result #2501198

Information on Result #2501198

Linear OOA(4²⁵⁷, 462, F₄, 2, 81) (dual of [(462, 2), 667, 82]-NRT-code), using 4¹ times duplication based on linear OOA(4²⁵⁶, 462, F₄, 2, 81) (dual of [(462, 2), 668, 82]-NRT-code), using

trace code [i] based on linear OOA(16¹²⁸, 231, F₁₆, 2, 81) (dual of [(231, 2), 334, 82]-NRT-code), using
- constructionÂ X applied to AG(2;F,366P) âŠ‚ AG(2;F,374P) [i] based on
  1. linear OOA(16¹²¹, 224, F₁₆, 2, 81) (dual of [(224, 2), 327, 82]-NRT-code), using algebraic-geometric NRT-code AG(2;F,366P) [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(16¹¹³, 224, F₁₆, 2, 73) (dual of [(224, 2), 335, 74]-NRT-code), using algebraic-geometric NRT-code AG(2;F,374P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225 (see above)
  3. linear OOA(16⁷, 7, F₁₆, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁷, 16, F₁₆, 2, 7) (dual of [(16, 2), 25, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;25,16) [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.