MinT - Information on Result #1765595

Information on Result #1765595

Digital (151, 169, 1373152)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶⁹, 1373152, F₃, 3, 18) (dual of [(1373152, 3), 4119287, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶⁹, 1594327, F₃, 3, 18) (dual of [(1594327, 3), 4782812, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁶⁹, 4782981, F₃, 18) (dual of [4782981, 4782812, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁶⁹, 4782983, F₃, 18) (dual of [4782983, 4782814, 19]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁷⁰, 4782984, F₃, 19) (dual of [4782984, 4782814, 20]-code), using
      - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
        linear OA(3¹⁶⁹, 4782969, F₃, 19) (dual of [4782969, 4782800, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
        linear OA(3¹⁵⁵, 4782969, F₃, 17) (dual of [4782969, 4782814, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(3¹, 15, F₃, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 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.