MinT - Information on Result #1060613

Information on Result #1060613

Linear OOA(3²²¹, 2097350, F₃, 4, 19) (dual of [(2097350, 4), 8389179, 20]-NRT-code), using OOA 2-folding based on linear OOA(3²²¹, 4194700, F₃, 2, 19) (dual of [(4194700, 2), 8389179, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²¹, 4194701, F₃, 2, 19) (dual of [(4194701, 2), 8389181, 20]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁴⁰, 400, F₃, 2, 9) (dual of [(400, 2), 760, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (31, 40, 400)-net over F₃, using
      - trace code for nets [i] based on digital (1, 10, 100)-net over F₈₁, using
        net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
  2. linear OOA(3¹⁸¹, 4194301, F₃, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁸¹, 8388602, F₃, 19) (dual of [8388602, 8388421, 20]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’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.