MinT - Information on Result #2478381

Information on Result #2478381

Linear OOA(2²¹⁶, 4325373, F₂, 2, 14) (dual of [(4325373, 2), 8650530, 15]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2²¹⁴, 4325372, F₂, 2, 14) (dual of [(4325372, 2), 8650530, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵³, 131071, F₂, 2, 7) (dual of [(131071, 2), 262089, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (46, 53, 131071)-net over F₂, using
    - nets constructed from net-embeddable BCH codes [i]
2. linear OOA(2¹⁶¹, 4194301, F₂, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹⁶¹, 8388602, F₂, 14) (dual of [8388602, 8388441, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(2²¹⁶, 3527069, F₂, 3, 14) (dual of [(3527069, 3), 10580991, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹⁶, 3527069, F₂, 4, 14) (dual of [(3527069, 4), 14108060, 15]-NRT-code)	[i]
3	Linear OOA(2²¹⁶, 3527069, F₂, 5, 14) (dual of [(3527069, 5), 17635129, 15]-NRT-code)	[i]
4	Linear OOA(2²¹⁶, 3527069, F₂, 6, 14) (dual of [(3527069, 6), 21162198, 15]-NRT-code)	[i]
5	Linear OOA(2²¹⁶, 3527069, F₂, 7, 14) (dual of [(3527069, 7), 24689267, 15]-NRT-code)	[i]
6	Linear OOA(2²¹⁶, 3527069, F₂, 8, 14) (dual of [(3527069, 8), 28216336, 15]-NRT-code)	[i]
7	Digital (202, 216, 3527069)-net over F₂	[i]