MinT - Information on Result #2798646

Information on Result #2798646

Linear OOA(3²¹⁷, 2097152, F₃, 4, 22) (dual of [(2097152, 4), 8388391, 23]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3²¹³, 2097151, F₃, 4, 22) (dual of [(2097151, 4), 8388391, 23]-NRT-code), using

OOA 2-folding [i] based on linear OOA(3²¹³, 4194302, F₃, 2, 22) (dual of [(4194302, 2), 8388391, 23]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3²¹¹, 4194301, F₃, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²¹¹, 8388602, F₃, 22) (dual of [8388602, 8388391, 23]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²¹¹, large, F₃, 22) (dual of [large, large−211, 23]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(3²¹⁸, 2097152, F₃, 4, 22) (dual of [(2097152, 4), 8388390, 23]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3²¹⁹, 2097152, F₃, 4, 22) (dual of [(2097152, 4), 8388389, 23]-NRT-code)	[i]
3	Linear OOA(3²²⁰, 2097152, F₃, 4, 22) (dual of [(2097152, 4), 8388388, 23]-NRT-code)	[i]
4	Linear OOA(3²¹⁷, 2097152, F₃, 5, 22) (dual of [(2097152, 5), 10485543, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Digital (195, 217, 2097152)-net over F₃	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound