MinT - Information on Result #859207

Information on Result #859207

Linear OOA(16⁷³, 43, F₁₆, 2, 57) (dual of [(43, 2), 13, 58]-NRT-code), using OOA 2-folding based on linear OA(16⁷³, 86, F₁₆, 57) (dual of [86, 13, 58]-code), using

1 times truncation [i] based on linear OA(16⁷⁴, 87, F₁₆, 58) (dual of [87, 13, 59]-code), using
- constructionÂ X applied to AG(F,5P) âŠ‚ AG(F,18P) [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(16⁵¹, 64, F₁₆, 45) (dual of [64, 13, 46]-code), using algebraic-geometric code AG(F,18P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16¹³, 23, F₁₆, 12) (dual of [23, 10, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹³, 24, F₁₆, 12) (dual of [24, 11, 13]-code), using
      - extended algebraic-geometric code AG_e(F,11P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, 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.