MinT - Information on Result #1777490

Information on Result #1777490

Digital (146, 166, 1537901)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁶⁶, 1537901, F₄, 2, 20) (dual of [(1537901, 2), 3075636, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁶⁶, 2097157, F₄, 2, 20) (dual of [(2097157, 2), 4194148, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁶⁶, 4194314, F₄, 20) (dual of [4194314, 4194148, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁶⁶, 4194315, F₄, 20) (dual of [4194315, 4194149, 21]-code), using
    - 1 times truncation [i] based on linear OA(4¹⁶⁷, 4194316, F₄, 21) (dual of [4194316, 4194149, 22]-code), using
      - constructionÂ X applied to C_e(20) âŠ‚ C_e(18) [i] based on
        linear OA(4¹⁶⁶, 4194304, F₄, 21) (dual of [4194304, 4194138, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(4¹⁵⁵, 4194304, F₄, 19) (dual of [4194304, 4194149, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
        linear OA(4¹, 12, F₄, 1) (dual of [12, 11, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.