MinT - Information on Result #859352

Information on Result #859352

Linear OOA(16⁷², 40, F₁₆, 2, 60) (dual of [(40, 2), 8, 61]-NRT-code), using OOA 2-folding based on linear OA(16⁷², 80, F₁₆, 60) (dual of [80, 8, 61]-code), using

2 times truncation [i] based on linear OA(16⁷⁴, 82, F₁₆, 62) (dual of [82, 8, 63]-code), using
- constructionÂ XX applied to AG(F,0P) âŠ‚ AG(F,12P) âŠ‚ AG(F,13P) [i] based on
  1. linear OA(16⁶³, 64, F₁₆, 63) (dual of [64, 1, 64]-code or 64-arc in PG(62,16)), using algebraic-geometric code AG(F,0P) [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(16⁵⁷, 64, F₁₆, 51) (dual of [64, 7, 52]-code), using algebraic-geometric code AG(F,12P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16⁵⁶, 64, F₁₆, 50) (dual of [64, 8, 51]-code), using algebraic-geometric code AG(F,13P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  4. linear OA(16¹⁰, 17, F₁₆, 10) (dual of [17, 7, 11]-code or 17-arc in PG(9,16)), using
    - extended Reedâ€“Solomon code RS_e(7,16) [i]
  5. linear OA(16⁰, 1, F₁₆, 0) (dual of [1, 1, 1]-code), using
    - dual of repetition code with length 1 [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.