MinT - Information on Result #2496293

Information on Result #2496293

Linear OOA(4¹⁹³, 524314, F₄, 2, 25) (dual of [(524314, 2), 1048435, 26]-NRT-code), using 4¹ times duplication based on linear OOA(4¹⁹², 524314, F₄, 2, 25) (dual of [(524314, 2), 1048436, 26]-NRT-code), using

OOA 2-folding [i] based on linear OA(4¹⁹², 1048628, F₄, 25) (dual of [1048628, 1048436, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4¹⁹¹, 1048627, F₄, 25) (dual of [1048627, 1048436, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
    1. linear OA(4¹⁸¹, 1048577, F₄, 25) (dual of [1048577, 1048396, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(4¹⁴¹, 1048577, F₄, 19) (dual of [1048577, 1048436, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’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, 50, F₄, 5) (dual of [50, 40, 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		This result only	Method
1	Linear OOA(4¹⁹³, 508970, F₄, 3, 25) (dual of [(508970, 3), 1526717, 26]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (168, 193, 508970)-net over F₄	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound