MinT - Information on Result #2700725

Information on Result #2700725

Linear OOA(8¹⁶⁷, 1034, F₈, 3, 48) (dual of [(1034, 3), 2935, 49]-NRT-code), using 8¹ times duplication based on linear OOA(8¹⁶⁶, 1034, F₈, 3, 48) (dual of [(1034, 3), 2936, 49]-NRT-code), using

trace code [i] based on linear OOA(64⁸³, 517, F₆₄, 3, 48) (dual of [(517, 3), 1468, 49]-NRT-code), using
- constructionÂ X applied to AG(3;F,1487P) âŠ‚ AG(3;F,1495P) [i] based on
  1. linear OOA(64⁷⁶, 512, F₆₄, 3, 48) (dual of [(512, 3), 1460, 49]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1487P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]
  2. linear OOA(64⁶⁸, 512, F₆₄, 3, 40) (dual of [(512, 3), 1468, 41]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1495P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
  3. linear OOA(64⁷, 5, F₆₄, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁷, 64, F₆₄, 3, 7) (dual of [(64, 3), 185, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;185,64) [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.