MinT - Information on Result #2689570

Information on Result #2689570

Linear OOA(4¹⁵⁸, 538, F₄, 3, 40) (dual of [(538, 3), 1456, 41]-NRT-code), using 4² times duplication based on linear OOA(4¹⁵⁶, 538, F₄, 3, 40) (dual of [(538, 3), 1458, 41]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(4¹⁵³, 537, F₄, 3, 40) (dual of [(537, 3), 1458, 41]-NRT-code), using
- trace code [i] based on linear OOA(64⁵¹, 179, F₆₄, 3, 40) (dual of [(179, 3), 486, 41]-NRT-code), using
  - constructionÂ X applied to AG(3;F,487P) âŠ‚ AG(3;F,492P) [i] based on
    1. linear OOA(64⁴⁷, 176, F₆₄, 3, 40) (dual of [(176, 3), 481, 41]-NRT-code), using algebraic-geometric NRT-code AG(3;F,487P) [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(64⁴², 176, F₆₄, 3, 35) (dual of [(176, 3), 486, 36]-NRT-code), using algebraic-geometric NRT-code AG(3;F,492P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
    3. linear OOA(64⁴, 3, F₆₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 3, 4) (dual of [(64, 3), 188, 5]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(3;188,64) [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.