MinT - Information on Result #859299

Information on Result #859299

Linear OOA(16⁶⁷, 36, F₁₆, 2, 59) (dual of [(36, 2), 5, 60]-NRT-code), using OOA 2-folding based on linear OA(16⁶⁷, 72, F₁₆, 59) (dual of [72, 5, 60]-code), using

discarding factors / shortening the dual code based on linear OA(16⁶⁷, 73, F₁₆, 59) (dual of [73, 6, 60]-code), using
- constructionÂ X applied to AG(F,4P) âŠ‚ AG(F,10P) [i] based on
  1. linear OA(16⁶², 64, F₁₆, 59) (dual of [64, 2, 60]-code), using algebraic-geometric code AG(F,4P) 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(16⁵⁸, 64, F₁₆, 53) (dual of [64, 6, 54]-code), using algebraic-geometric code AG(F,10P) with known gap numbers [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16⁵, 9, F₁₆, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,16)), using
    - discarding factors / shortening the dual code based on linear OA(16⁵, 16, F₁₆, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
      - Reedâ€“Solomon code RS(11,16) [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.