MinT - Information on Result #857884

Information on Result #857884

Linear OOA(16⁴⁴, 35, F₁₆, 2, 35) (dual of [(35, 2), 26, 36]-NRT-code), using OOA 2-folding based on linear OA(16⁴⁴, 70, F₁₆, 35) (dual of [70, 26, 36]-code), using

discarding factors / shortening the dual code based on linear OA(16⁴⁴, 71, F₁₆, 35) (dual of [71, 27, 36]-code), using
- constructionÂ X applied to AG(F,28P) âŠ‚ AG(F,32P) [i] based on
  1. linear OA(16⁴¹, 64, F₁₆, 35) (dual of [64, 23, 36]-code), using algebraic-geometric code AG(F,28P) [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(16³⁷, 64, F₁₆, 31) (dual of [64, 27, 32]-code), using algebraic-geometric code AG(F,32P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16³, 7, F₁₆, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,16) or 7-cap in PG(2,16)), using
    - discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
      - Reedâ€“Solomon code RS(13,16) [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.