MinT - Information on Result #2217479

Information on Result #2217479

Linear OA(16¹²⁵, 144, F₁₆, 87) (dual of [144, 19, 88]-code), using strength reduction based on linear OA(16¹²⁵, 144, F₁₆, 88) (dual of [144, 19, 89]-code), using

juxtaposition [i] based on
1. linear OA(16⁴⁶, 65, F₁₆, 40) (dual of [65, 19, 41]-code), using
  - extended algebraic-geometric code AG_e(F,24P) [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(16⁶⁰, 79, F₁₆, 47) (dual of [79, 19, 48]-code), using
  - constructionÂ X applied to AG(F,16P) âŠ‚ AG(F,24P) [i] based on
    1. linear OA(16⁵³, 64, F₁₆, 47) (dual of [64, 11, 48]-code), using algebraic-geometric code AG(F,16P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    2. linear OA(16⁴⁵, 64, F₁₆, 39) (dual of [64, 19, 40]-code), using algebraic-geometric code AG(F,24P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    3. linear OA(16⁷, 15, F₁₆, 7) (dual of [15, 8, 8]-code or 15-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.