MinT - Information on Result #909146

Information on Result #909146

Linear OOA(3¹⁹², 99, F₃, 2, 129) (dual of [(99, 2), 6, 130]-NRT-code), using juxtaposition based on

linear OOA(3⁴⁸, 27, F₃, 2, 33) (dual of [(27, 2), 6, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁴⁸, 54, F₃, 33) (dual of [54, 6, 34]-code), using
  - 2 times truncation [i] based on linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
      2. nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
        20 is the largest size of a cap in PG(4,Â 3) [i]
- algebraic-geometric NRT-code AG(2;F,20P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹³⁸, 72, F₃, 2, 95) (dual of [(72, 2), 6, 96]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(3⁶⁶, 36, F₃, 2, 47) (dual of [(36, 2), 6, 48]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(3¹⁹, 12, F₃, 2, 15) (dual of [(12, 2), 5, 16]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(3²³, 12, F₃, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
      - dual of repetition NRT-code with length 12 [i]
    3. linear OOA(3²⁴, 12, F₃, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [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.