MinT - Information on Result #807827

Information on Result #807827

Linear OOA(2²⁰⁵, 2072, F₂, 2, 32) (dual of [(2072, 2), 3939, 33]-NRT-code), using OOA 2-folding based on linear OA(2²⁰⁵, 4144, F₂, 32) (dual of [4144, 3939, 33]-code), using

strength reduction [i] based on linear OA(2²⁰⁵, 4144, F₂, 33) (dual of [4144, 3939, 34]-code), using
- constructionÂ X applied to C_e(32) âŠ‚ C_e(26) [i] based on
  1. linear OA(2¹⁹³, 4096, F₂, 33) (dual of [4096, 3903, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
  2. linear OA(2¹⁵⁷, 4096, F₂, 27) (dual of [4096, 3939, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  3. linear OA(2¹², 48, F₂, 5) (dual of [48, 36, 6]-code), using
    - adding a parity check bit [i] based on linear OA(2¹¹, 47, F₂, 4) (dual of [47, 36, 5]-code), using
      - extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F₂, using
        linear code embedding found in a computer search [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁰⁷, 2073, F₂, 2, 32) (dual of [(2073, 2), 3939, 33]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁰⁶, 2072, F₂, 2, 32) (dual of [(2072, 2), 3938, 33]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁵, 1452, F₂, 3, 32) (dual of [(1452, 3), 4151, 33]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2²⁰⁵, 1452, F₂, 4, 32) (dual of [(1452, 4), 5603, 33]-NRT-code)	[i]
5	Linear OOA(2²⁰⁵, 1452, F₂, 5, 32) (dual of [(1452, 5), 7055, 33]-NRT-code)	[i]
6	Linear OOA(2²⁰⁵, 1452, F₂, 6, 32) (dual of [(1452, 6), 8507, 33]-NRT-code)	[i]
7	Linear OOA(2²⁰⁵, 1452, F₂, 7, 32) (dual of [(1452, 7), 9959, 33]-NRT-code)	[i]
8	Linear OOA(2²⁰⁵, 1452, F₂, 8, 32) (dual of [(1452, 8), 11411, 33]-NRT-code)	[i]
9	Digital (173, 205, 1452)-net over F₂	[i]