MinT - Information on Result #2265855

Information on Result #2265855

Linear OA(3¹³⁸, 6603, F₃, 24) (dual of [6603, 6465, 25]-code), using 1 times code embedding in larger space based on linear OA(3¹³⁷, 6602, F₃, 24) (dual of [6602, 6465, 25]-code), using

constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
1. linear OA(3¹²⁹, 6562, F₃, 25) (dual of [6562, 6433, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
2. linear OA(3⁹⁷, 6562, F₃, 19) (dual of [6562, 6465, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’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, 40, F₃, 4) (dual of [40, 32, 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: 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		Method
1	Linear OOA(3¹³⁸, 4216, F₃, 2, 24) (dual of [(4216, 2), 8294, 25]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹³⁸, 4216, F₃, 3, 24) (dual of [(4216, 3), 12510, 25]-NRT-code)	[i]
3	Linear OOA(3¹³⁸, 4216, F₃, 4, 24) (dual of [(4216, 4), 16726, 25]-NRT-code)	[i]
4	Linear OOA(3¹³⁸, 4216, F₃, 5, 24) (dual of [(4216, 5), 20942, 25]-NRT-code)	[i]
5	Digital (114, 138, 4216)-net over F₃	[i]
6	Linear OOA(3¹³⁸, 2201, F₃, 3, 24) (dual of [(2201, 3), 6465, 25]-NRT-code)	[i]	OOA Folding