MinT - Information on Result #2271765

Information on Result #2271765

Linear OA(4⁵⁵, 135, F₄, 20) (dual of [135, 80, 21]-code), using 1 times code embedding in larger space based on linear OA(4⁵⁴, 134, F₄, 20) (dual of [134, 80, 21]-code), using

trace code [i] based on linear OA(16²⁷, 67, F₁₆, 20) (dual of [67, 40, 21]-code), using
- constructionÂ X applied to AG(F,43P) âŠ‚ AG(F,45P) [i] based on
  1. linear OA(16²⁶, 64, F₁₆, 20) (dual of [64, 38, 21]-code), using algebraic-geometric code AG(F,43P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]
  2. linear OA(16²⁴, 64, F₁₆, 18) (dual of [64, 40, 19]-code), using algebraic-geometric code AG(F,45P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.