MinT - Information on Result #831307

Information on Result #831307

Linear OOA(4²⁴¹, 212, F₄, 2, 82) (dual of [(212, 2), 183, 83]-NRT-code), using OOA 2-folding based on linear OA(4²⁴¹, 424, F₄, 82) (dual of [424, 183, 83]-code), using

strength reduction [i] based on linear OA(4²⁴¹, 424, F₄, 83) (dual of [424, 183, 84]-code), using
- concatenation of two codes [i] based on
  1. linear OA(64⁴⁵, 106, F₆₄, 41) (dual of [106, 61, 42]-code), using
    - constructionÂ X applied to AG(F,61P) âŠ‚ AG(F,63P) [i] based on
      1. 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, using
        a function field by SÃ©mirat [i]
      2. linear OA(64⁴², 103, F₆₄, 39) (dual of [103, 61, 40]-code), using algebraic-geometric code AG(F,63P) [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]
  2. linear OA(4¹, 4, F₄, 1) (dual of [4, 3, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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.