MinT - Information on Result #1776322

Information on Result #1776322

Digital (125, 147, 103920)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁴⁷, 103920, F₄, 2, 22) (dual of [(103920, 2), 207693, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁴⁷, 131077, F₄, 2, 22) (dual of [(131077, 2), 262007, 23]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4¹⁴⁶, 131077, F₄, 2, 22) (dual of [(131077, 2), 262008, 23]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁴⁶, 262154, F₄, 22) (dual of [262154, 262008, 23]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(4¹⁴⁵, 262153, F₄, 22) (dual of [262153, 262008, 23]-code), using
      - constructionÂ X applied to C_e(21) âŠ‚ C_e(20) [i] based on
        linear OA(4¹⁴⁵, 262144, F₄, 22) (dual of [262144, 261999, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(4¹³⁶, 262144, F₄, 21) (dual of [262144, 262008, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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.