MinT - Information on Result #1536853

Information on Result #1536853

Linear OOA(4¹³², 524314, F₄, 3, 17) (dual of [(524314, 3), 1572810, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹³², 524314, F₄, 2, 17) (dual of [(524314, 2), 1048496, 18]-NRT-code), using

OOA 2-folding [i] based on linear OA(4¹³², 1048628, F₄, 17) (dual of [1048628, 1048496, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4¹³¹, 1048627, F₄, 17) (dual of [1048627, 1048496, 18]-code), using
  - constructionÂ X applied to C([0,8]) âŠ‚ C([0,5]) [i] based on
    1. linear OA(4¹²¹, 1048577, F₄, 17) (dual of [1048577, 1048456, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    2. linear OA(4⁸¹, 1048577, F₄, 11) (dual of [1048577, 1048496, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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: 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(4¹³², 174771, F₄, 21, 17) (dual of [(174771, 21), 3670059, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row