MinT - Information on Result #1186903

Information on Result #1186903

Linear OOA(4¹⁹⁶, 932131, F₄, 21, 19) (dual of [(932131, 21), 19574555, 20]-NRT-code), using OOA 3-folding and stacking with additional row based on linear OOA(4¹⁹⁶, 2796394, F₄, 3, 19) (dual of [(2796394, 3), 8388986, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁹⁶, 2796396, F₄, 3, 19) (dual of [(2796396, 3), 8388992, 20]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4²⁷, 195, F₄, 3, 9) (dual of [(195, 3), 558, 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, 2796201, F₄, 3, 19) (dual of [(2796201, 3), 8388434, 20]-NRT-code), using
    - OOA 3-folding [i] 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.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (177, 196, 932131)-net over F₄	[i]		Net Defined by OOA