MinT - Information on Result #2666920

Information on Result #2666920

Linear OOA(2²¹³, 2861736, F₂, 3, 15) (dual of [(2861736, 3), 8584995, 16]-NRT-code), using 2¹ times duplication based on linear OOA(2²¹², 2861736, F₂, 3, 15) (dual of [(2861736, 3), 8584996, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵⁰, 65535, F₂, 3, 7) (dual of [(65535, 3), 196555, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁶², 2796201, F₂, 3, 15) (dual of [(2796201, 3), 8388441, 16]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(2²¹³, 2741246, F₂, 4, 15) (dual of [(2741246, 4), 10964771, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹³, 2741246, F₂, 5, 15) (dual of [(2741246, 5), 13706017, 16]-NRT-code)	[i]
3	Linear OOA(2²¹³, 2741246, F₂, 6, 15) (dual of [(2741246, 6), 16447263, 16]-NRT-code)	[i]
4	Linear OOA(2²¹³, 2741246, F₂, 7, 15) (dual of [(2741246, 7), 19188509, 16]-NRT-code)	[i]
5	Linear OOA(2²¹³, 2741246, F₂, 8, 15) (dual of [(2741246, 8), 21929755, 16]-NRT-code)	[i]
6	Digital (198, 213, 2741246)-net over F₂	[i]