MinT - Information on Result #2498071

Information on Result #2498071

Linear OOA(4¹⁶⁷, 544, F₄, 2, 43) (dual of [(544, 2), 921, 44]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹⁶⁵, 543, F₄, 2, 43) (dual of [(543, 2), 921, 44]-NRT-code), using

trace code [i] based on linear OOA(64⁵⁵, 181, F₆₄, 2, 43) (dual of [(181, 2), 307, 44]-NRT-code), using
- constructionÂ X applied to AG(2;F,308P) âŠ‚ AG(2;F,314P) [i] based on
  1. linear OOA(64⁵⁰, 176, F₆₄, 2, 43) (dual of [(176, 2), 302, 44]-NRT-code), using algebraic-geometric NRT-code AG(2;F,308P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(64⁴⁴, 176, F₆₄, 2, 37) (dual of [(176, 2), 308, 38]-NRT-code), using algebraic-geometric NRT-code AG(2;F,314P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁵, 5, F₆₄, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁵, 64, F₆₄, 2, 5) (dual of [(64, 2), 123, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;123,64) [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.