MinT - Information on Result #2701123

Information on Result #2701123

Linear OOA(8¹⁵³, 364, F₈, 3, 60) (dual of [(364, 3), 939, 61]-NRT-code), using 8¹ times duplication based on linear OOA(8¹⁵², 364, F₈, 3, 60) (dual of [(364, 3), 940, 61]-NRT-code), using

trace code [i] based on linear OOA(64⁷⁶, 182, F₆₄, 3, 60) (dual of [(182, 3), 470, 61]-NRT-code), using
- constructionÂ X applied to AG(3;F,467P) âŠ‚ AG(3;F,477P) [i] based on
  1. linear OOA(64⁶⁷, 176, F₆₄, 3, 60) (dual of [(176, 3), 461, 61]-NRT-code), using algebraic-geometric NRT-code AG(3;F,467P) [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(64⁵⁷, 176, F₆₄, 3, 50) (dual of [(176, 3), 471, 51]-NRT-code), using algebraic-geometric NRT-code AG(3;F,477P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁹, 6, F₆₄, 3, 9) (dual of [(6, 3), 9, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁹, 64, F₆₄, 3, 9) (dual of [(64, 3), 183, 10]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;183,64) [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.