MinT - Information on Result #2498168

Information on Result #2498168

Linear OOA(4¹⁶⁴, 538, F₄, 2, 44) (dual of [(538, 2), 912, 45]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹⁶², 537, F₄, 2, 44) (dual of [(537, 2), 912, 45]-NRT-code), using

trace code [i] based on linear OOA(64⁵⁴, 179, F₆₄, 2, 44) (dual of [(179, 2), 304, 45]-NRT-code), using
- constructionÂ X applied to AG(2;F,307P) âŠ‚ AG(2;F,311P) [i] based on
  1. 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, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(64⁴⁷, 176, F₆₄, 2, 40) (dual of [(176, 2), 305, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,311P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64³, 3, F₆₄, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64³, 64, F₆₄, 2, 3) (dual of [(64, 2), 125, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;125,64) [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.