MinT - Information on Result #2282149

Information on Result #2282149

Linear OA(8¹⁶¹, 1031, F₈, 51) (dual of [1031, 870, 52]-code), using 1 times code embedding in larger space based on linear OA(8¹⁶⁰, 1030, F₈, 51) (dual of [1030, 870, 52]-code), using

trace code [i] based on linear OA(64⁸⁰, 515, F₆₄, 51) (dual of [515, 435, 52]-code), using
- constructionÂ X applied to AG(F,460P) âŠ‚ AG(F,462P) [i] based on
  1. linear OA(64⁷⁹, 512, F₆₄, 51) (dual of [512, 433, 52]-code), using algebraic-geometric code AG(F,460P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]
  2. linear OA(64⁷⁷, 512, F₆₄, 49) (dual of [512, 435, 50]-code), using algebraic-geometric code AG(F,462P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (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.