MinT - Information on Result #2265273

Information on Result #2265273

Linear OA(3¹⁰⁶, 6603, F₃, 18) (dual of [6603, 6497, 19]-code), using 1 times code embedding in larger space based on linear OA(3¹⁰⁵, 6602, F₃, 18) (dual of [6602, 6497, 19]-code), using

constructionÂ X applied to C([0,9]) âŠ‚ C([0,6]) [i] based on
1. 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]
2. linear OA(3⁶⁵, 6562, F₃, 13) (dual of [6562, 6497, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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(3¹⁰⁶, 4584, F₃, 2, 18) (dual of [(4584, 2), 9062, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁰⁶, 4584, F₃, 3, 18) (dual of [(4584, 3), 13646, 19]-NRT-code)	[i]
3	Linear OOA(3¹⁰⁶, 4584, F₃, 4, 18) (dual of [(4584, 4), 18230, 19]-NRT-code)	[i]
4	Linear OOA(3¹⁰⁶, 4584, F₃, 5, 18) (dual of [(4584, 5), 22814, 19]-NRT-code)	[i]
5	Digital (88, 106, 4584)-net over F₃	[i]
6	Linear OOA(3¹⁰⁶, 2201, F₃, 3, 18) (dual of [(2201, 3), 6497, 19]-NRT-code)	[i]	OOA Folding