MinT - Information on Result #1411520

Information on Result #1411520

Linear OOA(3¹⁵³, 2172, F₃, 2, 30) (dual of [(2172, 2), 4191, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁵³, 2172, F₃, 30) (dual of [2172, 2019, 31]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁵³, 2228, F₃, 30) (dual of [2228, 2075, 31]-code), using
- 4 times code embedding in larger space [i] based on linear OA(3¹⁴⁹, 2224, F₃, 30) (dual of [2224, 2075, 31]-code), using
  - constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(3¹⁴¹, 2188, F₃, 31) (dual of [2188, 2047, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
    2. linear OA(3¹¹³, 2188, F₃, 25) (dual of [2188, 2075, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    3. linear OA(3⁸, 36, F₃, 4) (dual of [36, 28, 5]-code), using
      - discarding factors / shortening the dual code based on 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(3¹⁵³, 1086, F₃, 3, 30) (dual of [(1086, 3), 3105, 31]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁵³, 1086, F₃, 4, 30) (dual of [(1086, 4), 4191, 31]-NRT-code)	[i]		OOA Folding