MinT - Information on Result #1816380

Information on Result #1816380

OA(32¹², 82, S₃₂, 8), using discarding parts of the base based on linear OA(64¹⁰, 82, F₆₄, 8) (dual of [82, 72, 9]-code), using

constructionÂ X applied to AG(F,70P) âŠ‚ AG(F,72P) [i] based on
1. linear OA(64⁹, 79, F₆₄, 8) (dual of [79, 70, 9]-code), using algebraic-geometric code AG(F,70P) [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(64⁷, 79, F₆₄, 6) (dual of [79, 72, 7]-code), using algebraic-geometric code AG(F,72P) [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]

Mode: Constructive.

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.