MinT - Information on Result #1788754

Information on Result #1788754

Digital (114, 137, 72947)-net over F₅, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(5¹³⁷, 72947, F₅, 23) (dual of [72947, 72810, 24]-code), using

discarding factors / shortening the dual code based on linear OA(5¹³⁷, 78164, F₅, 23) (dual of [78164, 78027, 24]-code), using
- constructionÂ X applied to C([0,11]) âŠ‚ C([0,8]) [i] based on
  1. linear OA(5¹²⁷, 78126, F₅, 23) (dual of [78126, 77999, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126Â | 5¹⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
  2. linear OA(5⁹⁹, 78126, F₅, 17) (dual of [78126, 78027, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126Â | 5¹⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
  3. linear OA(5¹⁰, 38, F₅, 5) (dual of [38, 28, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹⁰, 52, F₅, 5) (dual of [52, 42, 6]-code), using
      - trace code [i] based on linear OA(25⁵, 26, F₂₅, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
        extended Reedâ€“Solomon code RS_e(21,25) [i]
        the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
        algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
        algebraic-geometric code AG(F, Q+6P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.