MinT - Information on Result #1777230

Information on Result #1777230

Digital (134, 162, 16441)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4¹⁶², 16441, F₄, 28) (dual of [16441, 16279, 29]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(4¹⁶¹, 16439, F₄, 28) (dual of [16439, 16278, 29]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(20) [i] based on
    1. linear OA(4¹⁴⁸, 16384, F₄, 29) (dual of [16384, 16236, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. linear OA(4¹⁰⁶, 16384, F₄, 21) (dual of [16384, 16278, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(4¹³, 55, F₄, 6) (dual of [55, 42, 7]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹³, 63, F₄, 6) (dual of [63, 50, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
2. linear OA(4¹⁶¹, 16440, F₄, 27) (dual of [16440, 16279, 28]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹⁶¹Â > V_b^sâˆ’1(kâˆ’1)Â = 253473 623195 315634 881111 504064 189772 532525 068509 905644 918699 106368 238159 232919 363416 735410 177884 [i]
3. linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [i]

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.