MinT - Information on Result #1132819

Information on Result #1132819

Linear OOA(2²⁴¹, 10925, F₂, 6, 30) (dual of [(10925, 6), 65309, 31]-NRT-code), using OOA 6-folding based on linear OA(2²⁴¹, 65550, F₂, 30) (dual of [65550, 65309, 31]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁴¹, 65552, F₂, 30) (dual of [65552, 65311, 31]-code), using
- 1 times truncation [i] based on linear OA(2²⁴², 65553, F₂, 31) (dual of [65553, 65311, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
    1. linear OA(2²⁴¹, 65536, F₂, 31) (dual of [65536, 65295, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(2²²⁵, 65536, F₂, 29) (dual of [65536, 65311, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(2²⁴³, 10925, F₂, 6, 30) (dual of [(10925, 6), 65307, 31]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁴¹, 10925, F₂, 7, 30) (dual of [(10925, 7), 76234, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2²⁴¹, 10925, F₂, 8, 30) (dual of [(10925, 8), 87159, 31]-NRT-code)	[i]
4	Digital (211, 241, 10925)-net over F₂	[i]