MinT - Information on Result #1096587

Information on Result #1096587

Linear OOA(2²²⁰, 13116, F₂, 5, 26) (dual of [(13116, 5), 65360, 27]-NRT-code), using OOA 5-folding based on linear OA(2²²⁰, 65580, F₂, 26) (dual of [65580, 65360, 27]-code), using

discarding factors / shortening the dual code based on linear OA(2²²⁰, 65583, F₂, 26) (dual of [65583, 65363, 27]-code), using
- 1 times truncation [i] based on linear OA(2²²¹, 65584, F₂, 27) (dual of [65584, 65363, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(20) [i] based on
    1. linear OA(2²⁰⁹, 65536, F₂, 27) (dual of [65536, 65327, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(2¹⁶¹, 65536, F₂, 21) (dual of [65536, 65375, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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(2²²⁰, 13116, F₂, 6, 26) (dual of [(13116, 6), 78476, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²²⁰, 13116, F₂, 7, 26) (dual of [(13116, 7), 91592, 27]-NRT-code)	[i]
3	Linear OOA(2²²⁰, 13116, F₂, 8, 26) (dual of [(13116, 8), 104708, 27]-NRT-code)	[i]
4	Digital (194, 220, 13116)-net over F₂	[i]