MinT - Information on Result #2265589

Information on Result #2265589

Linear OA(3¹²², 6602, F₃, 21) (dual of [6602, 6480, 22]-code), using 1 times code embedding in larger space based on linear OA(3¹²¹, 6601, F₃, 21) (dual of [6601, 6480, 22]-code), using

constructionÂ X applied to C_e(21) âŠ‚ C_e(15) [i] based on
1. linear OA(3¹¹³, 6561, F₃, 22) (dual of [6561, 6448, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
2. linear OA(3⁸¹, 6561, F₃, 16) (dual of [6561, 6480, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(3¹²², 4314, F₃, 2, 21) (dual of [(4314, 2), 8506, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹²², 4314, F₃, 3, 21) (dual of [(4314, 3), 12820, 22]-NRT-code)	[i]
3	Linear OOA(3¹²², 4314, F₃, 4, 21) (dual of [(4314, 4), 17134, 22]-NRT-code)	[i]
4	Linear OOA(3¹²², 4314, F₃, 5, 21) (dual of [(4314, 5), 21448, 22]-NRT-code)	[i]
5	Digital (101, 122, 4314)-net over F₃	[i]
6	Linear OOA(3¹²², 3301, F₃, 2, 21) (dual of [(3301, 2), 6480, 22]-NRT-code)	[i]	OOA Folding