MinT - Information on Result #859151

Information on Result #859151

Linear OOA(16⁶⁶, 37, F₁₆, 2, 56) (dual of [(37, 2), 8, 57]-NRT-code), using OOA 2-folding based on linear OA(16⁶⁶, 74, F₁₆, 56) (dual of [74, 8, 57]-code), using

2 times truncation [i] based on linear OA(16⁶⁸, 76, F₁₆, 58) (dual of [76, 8, 59]-code), using
- constructionÂ X applied to AG(F,5P) âŠ‚ AG(F,13P) [i] based on
  1. 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]
  2. 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)
  3. linear OA(16⁷, 12, F₁₆, 7) (dual of [12, 5, 8]-code or 12-arc in PG(6,16)), using
    - discarding factors / shortening the dual code based on linear OA(16⁷, 16, F₁₆, 7) (dual of [16, 9, 8]-code or 16-arc in PG(6,16)), using
      - Reedâ€“Solomon code RS(9,16) [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.