MinT - Information on Result #967418

Information on Result #967418

Linear OOA(4²⁶⁰, 272, F₄, 3, 74) (dual of [(272, 3), 556, 75]-NRT-code), using OOA 2-folding based on linear OOA(4²⁶⁰, 544, F₄, 2, 74) (dual of [(544, 2), 828, 75]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(4²⁵⁸, 543, F₄, 2, 74) (dual of [(543, 2), 828, 75]-NRT-code), using
- trace code [i] based on linear OOA(64⁸⁶, 181, F₆₄, 2, 74) (dual of [(181, 2), 276, 75]-NRT-code), using
  - constructionÂ X applied to AG(2;F,277P) âŠ‚ AG(2;F,283P) [i] based on
    1. linear OOA(64⁸¹, 176, F₆₄, 2, 74) (dual of [(176, 2), 271, 75]-NRT-code), using algebraic-geometric NRT-code AG(2;F,277P) [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(64⁷⁵, 176, F₆₄, 2, 68) (dual of [(176, 2), 277, 69]-NRT-code), using algebraic-geometric NRT-code AG(2;F,283P) [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.