MinT - Information on Result #826662

Information on Result #826662

Linear OOA(4¹⁴¹, 159, F₄, 2, 43) (dual of [(159, 2), 177, 44]-NRT-code), using OOA 2-folding based on linear OA(4¹⁴¹, 318, F₄, 43) (dual of [318, 177, 44]-code), using

trace code [i] based on linear OA(64⁴⁷, 106, F₆₄, 43) (dual of [106, 59, 44]-code), using
- constructionÂ X applied to AG(F,59P) âŠ‚ AG(F,61P) [i] based on
  1. linear OA(64⁴⁶, 103, F₆₄, 43) (dual of [103, 57, 44]-code), using algebraic-geometric code AG(F,59P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]
  2. linear OA(64⁴⁴, 103, F₆₄, 41) (dual of [103, 59, 42]-code), using algebraic-geometric code AG(F,61P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104 (see above)
  3. linear OA(64¹, 3, F₆₄, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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.