MinT - Information on Result #858961

Information on Result #858961

Linear OOA(16⁸³, 55, F₁₆, 2, 52) (dual of [(55, 2), 27, 53]-NRT-code), using OOA 2-folding based on linear OA(16⁸³, 110, F₁₆, 52) (dual of [110, 27, 53]-code), using

1 times truncation [i] based on linear OA(16⁸⁴, 111, F₁₆, 53) (dual of [111, 27, 54]-code), using
- constructionÂ X applied to AG(F,10P) âŠ‚ AG(F,32P) [i] based on
  1. 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, 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(16²⁶, 47, F₁₆, 21) (dual of [47, 21, 22]-code), using
    - discarding factors / shortening the dual code based on linear OA(16²⁶, 49, F₁₆, 21) (dual of [49, 23, 22]-code), using
      - extended algebraic-geometric code AG_e(F,27P) [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
        a function field by SÃ©mirat [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.