MinT - Information on Result #2798072

Information on Result #2798072

Linear OOA(3¹⁷⁴, 2097206, F₃, 4, 16) (dual of [(2097206, 4), 8388650, 17]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁷³, 2097206, F₃, 4, 16) (dual of [(2097206, 4), 8388651, 17]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²², 56, F₃, 4, 8) (dual of [(56, 4), 202, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (14, 22, 56)-net over F₃, using
    - trace code for nets [i] based on digital (3, 11, 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(3¹⁵¹, 2097150, F₃, 4, 16) (dual of [(2097150, 4), 8388449, 17]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(3¹⁵¹, 8388600, F₃, 16) (dual of [8388600, 8388449, 17]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.