MinT - Information on Result #2498655

Information on Result #2498655

Linear OOA(4¹⁸², 541, F₄, 2, 49) (dual of [(541, 2), 900, 50]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹⁸⁰, 540, F₄, 2, 49) (dual of [(540, 2), 900, 50]-NRT-code), using

trace code [i] based on linear OOA(64⁶⁰, 180, F₆₄, 2, 49) (dual of [(180, 2), 300, 50]-NRT-code), using
- constructionÂ X applied to AG(2;F,302P) âŠ‚ AG(2;F,307P) [i] based on
  1. linear OOA(64⁵⁶, 176, F₆₄, 2, 49) (dual of [(176, 2), 296, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,302P) [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(64⁵¹, 176, F₆₄, 2, 44) (dual of [(176, 2), 301, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,307P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁴, 4, F₆₄, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 2, 4) (dual of [(64, 2), 124, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;124,64) [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.