MinT - Information on Result #1610514

Information on Result #1610514

Linear OOA(3²²², 531463, F₃, 4, 24) (dual of [(531463, 4), 2125630, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²², 531463, F₃, 3, 24) (dual of [(531463, 3), 1594167, 25]-NRT-code), using

strength reduction [i] based on linear OOA(3²²², 531463, F₃, 3, 25) (dual of [(531463, 3), 1594167, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²²², 1594389, F₃, 25) (dual of [1594389, 1594167, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
    1. linear OA(3²⁰⁹, 1594324, F₃, 25) (dual of [1594324, 1594115, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(3¹⁵⁷, 1594324, F₃, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    3. linear OA(3¹³, 65, F₃, 5) (dual of [65, 52, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹³, 80, F₃, 5) (dual of [80, 67, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,4], 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(3²²³, 531463, F₃, 4, 24) (dual of [(531463, 4), 2125629, 25]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²²², 177154, F₃, 28, 24) (dual of [(177154, 28), 4960090, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row