MinT - Information on Result #859223

Information on Result #859223

Linear OOA(16⁹⁶, 65, F₁₆, 2, 57) (dual of [(65, 2), 34, 58]-NRT-code), using OOA 2-folding based on linear OA(16⁹⁶, 130, F₁₆, 57) (dual of [130, 34, 58]-code), using

discarding factors / shortening the dual code based on linear OA(16⁹⁶, 131, F₁₆, 57) (dual of [131, 35, 58]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16³⁴, 65, F₁₆, 28) (dual of [65, 31, 29]-code), using
    - extended algebraic-geometric code AG_e(F,36P) [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(16⁶², 66, F₁₆, 57) (dual of [66, 4, 58]-code), using
    - 1 times truncation [i] based on linear OA(16⁶³, 67, F₁₆, 58) (dual of [67, 4, 59]-code), using
      - constructionÂ X applied to AG(F,5P) âŠ‚ AG(F,8P) [i] based on
        linear OA(16⁶¹, 64, F₁₆, 58) (dual of [64, 3, 59]-code), using algebraic-geometric code AG(F,5P) with known gap numbers [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using the Hermitian function field over F₁₆ [i]
        linear OA(16⁶⁰, 64, F₁₆, 55) (dual of [64, 4, 56]-code), using algebraic-geometric code AG(F,8P) with known gap numbers [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
        linear OA(16², 3, F₁₆, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,16)), using
        dual of repetition code with length 3 [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.