MinT - Information on Result #1788400

Information on Result #1788400

Digital (108, 130, 66913)-net over F₅, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(5¹³⁰, 66913, F₅, 22) (dual of [66913, 66783, 23]-code), using

discarding factors / shortening the dual code based on linear OA(5¹³⁰, 78170, F₅, 22) (dual of [78170, 78040, 23]-code), using
- constructionÂ X applied to C_e(21) âŠ‚ C_e(15) [i] based on
  1. linear OA(5¹²⁰, 78125, F₅, 22) (dual of [78125, 78005, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
  2. linear OA(5⁸⁵, 78125, F₅, 16) (dual of [78125, 78040, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  3. linear OA(5¹⁰, 45, F₅, 5) (dual of [45, 35, 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.