MinT - Information on Result #1781736

Information on Result #1781736

Digital (193, 222, 437024)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²²², 437024, F₄, 2, 29) (dual of [(437024, 2), 873826, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²²², 524313, F₄, 2, 29) (dual of [(524313, 2), 1048404, 30]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4²²¹, 524313, F₄, 2, 29) (dual of [(524313, 2), 1048405, 30]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²²¹, 1048626, F₄, 29) (dual of [1048626, 1048405, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(22) [i] based on
      1. linear OA(4²¹¹, 1048576, F₄, 29) (dual of [1048576, 1048365, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(4¹⁷¹, 1048576, F₄, 23) (dual of [1048576, 1048405, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(4¹⁰, 50, F₄, 5) (dual of [50, 40, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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.