MinT - Information on Result #875434

Information on Result #875434

Linear OOA(64⁵³, 89, F₆₄, 2, 45) (dual of [(89, 2), 125, 46]-NRT-code), using OOA 2-folding based on linear OA(64⁵³, 178, F₆₄, 45) (dual of [178, 125, 46]-code), using

discarding factors / shortening the dual code based on linear OA(64⁵³, 179, F₆₄, 45) (dual of [179, 126, 46]-code), using
- constructionÂ X applied to AG(F,130P) âŠ‚ AG(F,132P) [i] based on
  1. linear OA(64⁵², 176, F₆₄, 45) (dual of [176, 124, 46]-code), using algebraic-geometric code AG(F,130P) [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(64⁵⁰, 176, F₆₄, 43) (dual of [176, 126, 44]-code), using algebraic-geometric code AG(F,132P) [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.