MinT - Information on Result #1776988

Information on Result #1776988

Digital (139, 158, 1680735)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁵⁸, 1680735, F₄, 2, 19) (dual of [(1680735, 2), 3361312, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁵⁸, 2097165, F₄, 2, 19) (dual of [(2097165, 2), 4194172, 20]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4¹⁵⁷, 2097165, F₄, 2, 19) (dual of [(2097165, 2), 4194173, 20]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁵⁷, 4194330, F₄, 19) (dual of [4194330, 4194173, 20]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(4¹⁵⁶, 4194329, F₄, 19) (dual of [4194329, 4194173, 20]-code), using
      - constructionÂ X4 applied to C([0,9]) âŠ‚ C([0,8]) [i] based on
        linear OA(4¹⁵⁵, 4194305, F₄, 19) (dual of [4194305, 4194150, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305Â | 4²²âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
        linear OA(4¹³³, 4194305, F₄, 17) (dual of [4194305, 4194172, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305Â | 4²²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
        linear OA(4²³, 24, F₄, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
        dual of repetition code with length 24 [i]
        linear OA(4¹, 24, F₄, 1) (dual of [24, 23, 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.