MinT - Information on Result #965860

Information on Result #965860

Linear OOA(4¹⁷⁴, 109, F₄, 3, 58) (dual of [(109, 3), 153, 59]-NRT-code), using OOA 3-folding based on linear OA(4¹⁷⁴, 327, F₄, 58) (dual of [327, 153, 59]-code), using

1 times truncation [i] based on linear OA(4¹⁷⁵, 328, F₄, 59) (dual of [328, 153, 60]-code), using
- concatenation of two codes [i] based on
  1. linear OA(64³¹, 82, F₆₄, 29) (dual of [82, 51, 30]-code), using
    - constructionÂ X applied to AG(F,49P) âŠ‚ AG(F,51P) [i] based on
      1. linear OA(64³⁰, 79, F₆₄, 29) (dual of [79, 49, 30]-code), using algebraic-geometric code AG(F,49P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
      2. linear OA(64²⁸, 79, F₆₄, 27) (dual of [79, 51, 28]-code), using algebraic-geometric code AG(F,51P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80 (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.