MinT - Information on Result #828419

Information on Result #828419

Linear OOA(4¹⁸⁶, 195, F₄, 2, 56) (dual of [(195, 2), 204, 57]-NRT-code), using OOA 2-folding based on linear OA(4¹⁸⁶, 390, F₄, 56) (dual of [390, 204, 57]-code), using

trace code [i] based on linear OA(64⁶², 130, F₆₄, 56) (dual of [130, 68, 57]-code), using
- constructionÂ X applied to AG(F,70P) âŠ‚ AG(F,72P) [i] based on
  1. linear OA(64⁶¹, 127, F₆₄, 56) (dual of [127, 66, 57]-code), using algebraic-geometric code AG(F,70P) [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]
  2. linear OA(64⁵⁹, 127, F₆₄, 54) (dual of [127, 68, 55]-code), using algebraic-geometric code AG(F,72P) [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128 (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.