MinT - Information on Result #2500098

Information on Result #2500098

Linear OOA(4²⁵¹, 565, F₄, 2, 64) (dual of [(565, 2), 879, 65]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²⁴⁹, 564, F₄, 2, 64) (dual of [(564, 2), 879, 65]-NRT-code), using

trace code [i] based on linear OOA(64⁸³, 188, F₆₄, 2, 64) (dual of [(188, 2), 293, 65]-NRT-code), using
- constructionÂ X applied to AG(2;F,287P) âŠ‚ AG(2;F,300P) [i] based on
  1. linear OOA(64⁷¹, 176, F₆₄, 2, 64) (dual of [(176, 2), 281, 65]-NRT-code), using algebraic-geometric NRT-code AG(2;F,287P) [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(64⁵⁸, 176, F₆₄, 2, 51) (dual of [(176, 2), 294, 52]-NRT-code), using algebraic-geometric NRT-code AG(2;F,300P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64¹², 12, F₆₄, 2, 12) (dual of [(12, 2), 12, 13]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹², 64, F₆₄, 2, 12) (dual of [(64, 2), 116, 13]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;116,64) [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.