MinT - Information on Result #2687729

Information on Result #2687729

Linear OOA(4²³⁶, 2796715, F₄, 3, 22) (dual of [(2796715, 3), 8389909, 23]-NRT-code), using 4¹ times duplication based on linear OOA(4²³⁵, 2796715, F₄, 3, 22) (dual of [(2796715, 3), 8389910, 23]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4⁴², 514, F₄, 3, 11) (dual of [(514, 3), 1500, 12]-NRT-code), using
  - extracting embedded OOA [i] based on digital (31, 42, 514)-net over F₄, using
    - trace code for nets [i] based on digital (10, 21, 257)-net over F₁₆, using
      - base reduction for projective spaces (embedding PG(10,256) in PG(20,16)) for nets [i] based on digital (0, 11, 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]
2. linear OOA(4¹⁹³, 2796201, F₄, 3, 22) (dual of [(2796201, 3), 8388410, 23]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(4¹⁹³, large, F₄, 22) (dual of [large, large−193, 23]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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.