MinT - Information on Result #1059857

Information on Result #1059857

Linear OOA(3¹²³, 2097151, F₃, 4, 13) (dual of [(2097151, 4), 8388481, 14]-NRT-code), using OOA 2-folding based on linear OOA(3¹²³, 4194302, F₃, 2, 13) (dual of [(4194302, 2), 8388481, 14]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3¹²¹, 4194301, F₃, 2, 13) (dual of [(4194301, 2), 8388481, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹²¹, 8388602, F₃, 13) (dual of [8388602, 8388481, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹²³, 2097151, F₃, 4, 12) (dual of [(2097151, 4), 8388481, 13]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹²⁴, 2097151, F₃, 4, 13) (dual of [(2097151, 4), 8388480, 14]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3¹²⁵, 2097151, F₃, 4, 13) (dual of [(2097151, 4), 8388479, 14]-NRT-code)	[i]
4	Linear OOA(3¹²⁶, 2097151, F₃, 4, 13) (dual of [(2097151, 4), 8388478, 14]-NRT-code)	[i]
5	Linear OOA(3¹³⁶, 2097193, F₃, 4, 13) (dual of [(2097193, 4), 8388636, 14]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
6	Linear OOA(3¹⁴⁷, 2097479, F₃, 4, 13) (dual of [(2097479, 4), 8389769, 14]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs