MinT - Information on Result #2690366

Information on Result #2690366

Linear OOA(4²⁴⁴, 1548, F₄, 3, 47) (dual of [(1548, 3), 4400, 48]-NRT-code), using 4¹ times duplication based on linear OOA(4²⁴³, 1548, F₄, 3, 47) (dual of [(1548, 3), 4401, 48]-NRT-code), using

trace code [i] based on linear OOA(64⁸¹, 516, F₆₄, 3, 47) (dual of [(516, 3), 1467, 48]-NRT-code), using
- constructionÂ X applied to AG(3;F,1488P) âŠ‚ AG(3;F,1495P) [i] based on
  1. linear OOA(64⁷⁵, 512, F₆₄, 3, 47) (dual of [(512, 3), 1461, 48]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1488P) [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(64⁶, 4, F₆₄, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁶, 64, F₆₄, 3, 6) (dual of [(64, 3), 186, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;186,64) [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.