MinT - Information on Result #824209

Information on Result #824209

Linear OOA(4²¹⁰, 2097180, F₄, 2, 25) (dual of [(2097180, 2), 4194150, 26]-NRT-code), using OOA 2-folding based on linear OA(4²¹⁰, 4194360, F₄, 25) (dual of [4194360, 4194150, 26]-code), using

1 times code embedding in larger space [i] 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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(4²¹¹, 2097180, F₄, 2, 25) (dual of [(2097180, 2), 4194149, 26]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(4²¹⁰, 1485697, F₄, 3, 25) (dual of [(1485697, 3), 4456881, 26]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Digital (185, 210, 1485697)-net over F₄	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound