MinT - Information on Result #1186706

Information on Result #1186706

Digital (164, 181, 1049087)-net over F₄, using net defined by OOA based on linear OOA(4¹⁸¹, 1049087, F₄, 18, 17) (dual of [(1049087, 18), 18883385, 18]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(4¹⁸¹, 4196349, F₄, 2, 17) (dual of [(4196349, 2), 8392517, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4³⁶, 2048, F₄, 2, 8) (dual of [(2048, 2), 4060, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(4³⁶, 4096, F₄, 8) (dual of [4096, 4060, 9]-code), using
      - 1 times truncation [i] based on linear OA(4³⁷, 4097, F₄, 9) (dual of [4097, 4060, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 4097Â | 4¹²âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
  2. linear OOA(4¹⁴⁵, 4194301, F₄, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(4¹⁴⁵, 8388602, F₄, 17) (dual of [8388602, 8388457, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁴⁵, large, F₄, 17) (dual of [large, large−145, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive and 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.