MinT - Information on Result #2677129

Information on Result #2677129

Linear OOA(3²⁴⁹, 3188702, F₃, 3, 18) (dual of [(3188702, 3), 9565857, 19]-NRT-code), using 3¹ times duplication based on linear OOA(3²⁴⁸, 3188702, F₃, 3, 18) (dual of [(3188702, 3), 9565858, 19]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²⁴, 56, F₃, 3, 9) (dual of [(56, 3), 144, 10]-NRT-code), using
  - extracting embedded OOA [i] based on digital (15, 24, 56)-net over F₃, using
    - trace code for nets [i] based on digital (3, 12, 28)-net over F₉, using
      - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
        the Hermitian function field over F₉ [i]
2. linear OOA(3²²⁴, 3188646, F₃, 3, 18) (dual of [(3188646, 3), 9565714, 19]-NRT-code), using
  - trace code [i] based on linear OOA(9¹¹², 1594323, F₉, 3, 18) (dual of [(1594323, 3), 4782857, 19]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(9¹¹², 4782969, F₉, 18) (dual of [4782969, 4782857, 19]-code), using
      - 1 times truncation [i] based on linear OA(9¹¹³, 4782970, F₉, 19) (dual of [4782970, 4782857, 20]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 9¹⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (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.