MinT - Information on Result #1784829

Information on Result #1784829

Digital (217, 255, 104246)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²⁵⁵, 104246, F₄, 2, 38) (dual of [(104246, 2), 208237, 39]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²⁵⁵, 131077, F₄, 2, 38) (dual of [(131077, 2), 261899, 39]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4²⁵⁴, 131077, F₄, 2, 38) (dual of [(131077, 2), 261900, 39]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²⁵⁴, 262154, F₄, 38) (dual of [262154, 261900, 39]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(4²⁵³, 262153, F₄, 38) (dual of [262153, 261900, 39]-code), using
      - constructionÂ X applied to C_e(37) âŠ‚ C_e(36) [i] based on
        linear OA(4²⁵³, 262144, F₄, 38) (dual of [262144, 261891, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
        linear OA(4²⁴⁴, 262144, F₄, 37) (dual of [262144, 261900, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
        linear OA(4⁰, 9, F₄, 0) (dual of [9, 9, 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.