MinT - Information on Result #2498260

Information on Result #2498260

Linear OOA(4¹⁷³, 544, F₄, 2, 45) (dual of [(544, 2), 915, 46]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹⁷¹, 543, F₄, 2, 45) (dual of [(543, 2), 915, 46]-NRT-code), using

trace code [i] based on linear OOA(64⁵⁷, 181, F₆₄, 2, 45) (dual of [(181, 2), 305, 46]-NRT-code), using
- constructionÂ X applied to AG(2;F,306P) âŠ‚ AG(2;F,312P) [i] based on
  1. linear OOA(64⁵², 176, F₆₄, 2, 45) (dual of [(176, 2), 300, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,306P) [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(64⁴⁶, 176, F₆₄, 2, 39) (dual of [(176, 2), 306, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,312P) [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.