MinT - Information on Result #2495661

Information on Result #2495661

Linear OOA(4¹⁹⁸, 4194497, F₄, 2, 19) (dual of [(4194497, 2), 8388796, 20]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹⁹⁶, 4194496, F₄, 2, 19) (dual of [(4194496, 2), 8388796, 20]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4²⁷, 195, F₄, 2, 9) (dual of [(195, 2), 363, 10]-NRT-code), using
  - extracting embedded OOA [i] based on digital (18, 27, 195)-net over F₄, using
    - trace code for nets [i] based on digital (0, 9, 65)-net over F₆₄, using
      - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [i]
2. linear OOA(4¹⁶⁹, 4194301, F₄, 2, 19) (dual of [(4194301, 2), 8388433, 20]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁶⁹, 8388602, F₄, 19) (dual of [8388602, 8388433, 20]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁶⁹, large, F₄, 19) (dual of [large, large−169, 20]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’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.