MinT - Information on Result #827757

Information on Result #827757

Linear OOA(4¹⁷⁷, 268, F₄, 2, 51) (dual of [(268, 2), 359, 52]-NRT-code), using OOA 2-folding based on linear OA(4¹⁷⁷, 536, F₄, 51) (dual of [536, 359, 52]-code), using

discarding factors / shortening the dual code based on linear OA(4¹⁷⁷, 537, F₄, 51) (dual of [537, 360, 52]-code), using
- trace code [i] based on linear OA(64⁵⁹, 179, F₆₄, 51) (dual of [179, 120, 52]-code), using
  - constructionÂ X applied to AG(F,124P) âŠ‚ AG(F,126P) [i] based on
    1. linear OA(64⁵⁸, 176, F₆₄, 51) (dual of [176, 118, 52]-code), using algebraic-geometric code AG(F,124P) [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 OA(64⁵⁶, 176, F₆₄, 49) (dual of [176, 120, 50]-code), using algebraic-geometric code AG(F,126P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (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.