MinT - Information on Result #1187414

Information on Result #1187414

Digital (184, 209, 349529)-net over F₄, using net defined by OOA based on linear OOA(4²⁰⁹, 349529, F₄, 25, 25) (dual of [(349529, 25), 8738016, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(4²⁰⁹, 4194349, F₄, 25) (dual of [4194349, 4194140, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4²⁰⁹, 4194359, F₄, 25) (dual of [4194359, 4194150, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
    1. linear OA(4¹⁹⁹, 4194305, F₄, 25) (dual of [4194305, 4194106, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305Â | 4²²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. 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]
    3. linear OA(4¹⁰, 54, F₄, 5) (dual of [54, 44, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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

The following results depend on this result:

	Result		This result only	Method
1	Digital (185, 210, 349529)-net over F₄	[i]		Net Duplication
2	Digital (184, 208, 349529)-net over F₄	[i]		m-Reduction