MinT - Information on Result #1011937

Information on Result #1011937

Linear OOA(4¹⁵⁹, 2796715, F₄, 3, 15) (dual of [(2796715, 3), 8389986, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4²⁶, 514, F₄, 3, 7) (dual of [(514, 3), 1516, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (19, 26, 514)-net over F₄, using
  - trace code for nets [i] based on digital (6, 13, 257)-net over F₁₆, using
    - base reduction for projective spaces (embedding PG(6,256) in PG(12,16)) for nets [i] based on digital (0, 7, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
linear OOA(4¹³³, 2796201, F₄, 3, 15) (dual of [(2796201, 3), 8388470, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4¹³³, large, F₄, 15) (dual of [large, large−133, 16]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁶⁰, 2796715, F₄, 3, 15) (dual of [(2796715, 3), 8389985, 16]-NRT-code)	[i]		OOA Duplication