MinT - Information on Result #2280817

Information on Result #2280817

Linear OA(8⁴¹, 213, F₈, 16) (dual of [213, 172, 17]-code), using 1 times code embedding in larger space based on linear OA(8⁴⁰, 212, F₈, 16) (dual of [212, 172, 17]-code), using

trace code [i] based on linear OA(64²⁰, 106, F₆₄, 16) (dual of [106, 86, 17]-code), using
- constructionÂ X applied to AG(F,86P) âŠ‚ AG(F,88P) [i] based on
  1. linear OA(64¹⁹, 103, F₆₄, 16) (dual of [103, 84, 17]-code), using algebraic-geometric code AG(F,86P) [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(64¹⁷, 103, F₆₄, 14) (dual of [103, 86, 15]-code), using algebraic-geometric code AG(F,88P) [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]

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.