MinT - Information on Result #1079954

Information on Result #1079954

Linear OOA(2²⁰³, 2105341, F₂, 4, 15) (dual of [(2105341, 4), 8421161, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴¹, 8191, F₂, 4, 7) (dual of [(8191, 4), 32723, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (34, 41, 8191)-net over F₂, using
  - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁶², 2097150, F₂, 4, 15) (dual of [(2097150, 4), 8388438, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹⁶², 8388600, F₂, 15) (dual of [8388600, 8388438, 16]-code), using
  - discarding factors / shortening the dual code 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.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁰³, 2105341, F₂, 4, 14) (dual of [(2105341, 4), 8421161, 15]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁰⁴, 2105341, F₂, 4, 15) (dual of [(2105341, 4), 8421160, 16]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰³, 2105341, F₂, 5, 15) (dual of [(2105341, 5), 10526502, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2²⁰³, 2105341, F₂, 6, 15) (dual of [(2105341, 6), 12631843, 16]-NRT-code)	[i]
5	Linear OOA(2²⁰³, 2105341, F₂, 7, 15) (dual of [(2105341, 7), 14737184, 16]-NRT-code)	[i]
6	Linear OOA(2²⁰³, 2105341, F₂, 8, 15) (dual of [(2105341, 8), 16842525, 16]-NRT-code)	[i]
7	Digital (188, 203, 2105341)-net over F₂	[i]