MinT - Information on Result #1081379

Information on Result #1081379

Linear OOA(3²³⁸, 2097479, F₃, 4, 20) (dual of [(2097479, 4), 8389678, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁴⁰, 328, F₃, 4, 10) (dual of [(328, 4), 1272, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (30, 40, 328)-net over F₃, using
  - trace code for nets [i] based on digital (0, 10, 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]
linear OOA(3¹⁹⁸, 2097151, F₃, 4, 20) (dual of [(2097151, 4), 8388406, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3¹⁹⁸, 4194302, F₃, 2, 20) (dual of [(4194302, 2), 8388406, 21]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁹⁶, 4194301, F₃, 2, 20) (dual of [(4194301, 2), 8388406, 21]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁹⁶, 8388602, F₃, 20) (dual of [8388602, 8388406, 21]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁹⁶, large, F₃, 20) (dual of [large, large−196, 21]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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.