MinT - Information on Result #1060208

Information on Result #1060208

Linear OOA(3¹⁷³, 2097178, F₃, 4, 16) (dual of [(2097178, 4), 8388539, 17]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁷³, 4194356, F₃, 2, 16) (dual of [(4194356, 2), 8388539, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁷³, 4194357, F₃, 2, 16) (dual of [(4194357, 2), 8388541, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3²², 56, F₃, 2, 8) (dual of [(56, 2), 90, 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, 4194301, F₃, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁵¹, 8388602, F₃, 16) (dual of [8388602, 8388451, 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.