MinT - Information on Result #2499830

Information on Result #2499830

Linear OOA(4²²⁴, 547, F₄, 2, 61) (dual of [(547, 2), 870, 62]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²²², 546, F₄, 2, 61) (dual of [(546, 2), 870, 62]-NRT-code), using

trace code [i] based on linear OOA(64⁷⁴, 182, F₆₄, 2, 61) (dual of [(182, 2), 290, 62]-NRT-code), using
- constructionÂ X applied to AG(2;F,290P) âŠ‚ AG(2;F,297P) [i] based on
  1. linear OOA(64⁶⁸, 176, F₆₄, 2, 61) (dual of [(176, 2), 284, 62]-NRT-code), using algebraic-geometric NRT-code AG(2;F,290P) [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(64⁶¹, 176, F₆₄, 2, 54) (dual of [(176, 2), 291, 55]-NRT-code), using algebraic-geometric NRT-code AG(2;F,297P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁶, 6, F₆₄, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁶, 64, F₆₄, 2, 6) (dual of [(64, 2), 122, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;122,64) [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.