MinT - Information on Result #1606310

Information on Result #1606310

Linear OOA(3¹⁶⁹, 27002, F₃, 4, 24) (dual of [(27002, 4), 107839, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶⁹, 27002, F₃, 2, 24) (dual of [(27002, 2), 53835, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶⁹, 29545, F₃, 2, 24) (dual of [(29545, 2), 58921, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁶⁹, 59090, F₃, 24) (dual of [59090, 58921, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁶⁹, 59091, F₃, 24) (dual of [59091, 58922, 25]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(3¹⁶¹, 59050, F₃, 25) (dual of [59050, 58889, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      2. linear OA(3¹²¹, 59050, F₃, 19) (dual of [59050, 58929, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(3⁸, 41, F₃, 4) (dual of [41, 33, 5]-code), using
        the narrow-sense BCH-code C(I) with length 41Â | 3⁸âˆ’1, defining interval IÂ =Â [1,1], and minimum distance dÂ â‰¥ |{−3,−1,1,3}|+1Â =Â 5 (BCH-bound) [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(3¹⁶⁹, 9000, F₃, 28, 24) (dual of [(9000, 28), 251831, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row