MinT - Information on Result #660630

Information on Result #660630

Linear OA(9¹⁰⁰, 744, F₉, 33) (dual of [744, 644, 34]-code), using trace code based on linear OA(81⁵⁰, 372, F₈₁, 33) (dual of [372, 322, 34]-code), using

constructionÂ X applied to AG(F,335P) âŠ‚ AG(F,337P) [i] based on
1. linear OA(81⁴⁹, 369, F₈₁, 33) (dual of [369, 320, 34]-code), using algebraic-geometric code AG(F,335P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
  - a function field by GarcÃa and Quoos [i]
2. linear OA(81⁴⁷, 369, F₈₁, 31) (dual of [369, 322, 32]-code), using algebraic-geometric code AG(F,337P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
3. linear OA(81¹, 3, F₈₁, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 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.