MinT - Information on Result #2797756

Information on Result #2797756

Linear OOA(3¹⁴⁴, 2097314, F₃, 4, 13) (dual of [(2097314, 4), 8389112, 14]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁴³, 2097314, F₃, 4, 13) (dual of [(2097314, 4), 8389113, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²², 164, F₃, 4, 6) (dual of [(164, 4), 634, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (16, 22, 164)-net over F₃, using
    - trace code for nets [i] based on digital (5, 11, 82)-net over F₉, using
      - base reduction for projective spaces (embedding PG(5,81) in PG(10,9)) for nets [i] based on digital (0, 6, 82)-net over F₈₁, using
        net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
        Niederreiter sequence [i]
2. linear OOA(3¹²¹, 2097150, F₃, 4, 13) (dual of [(2097150, 4), 8388479, 14]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(3¹²¹, 8388600, F₃, 13) (dual of [8388600, 8388479, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.