MinT - Information on Result #1164079

Information on Result #1164079

Linear OOA(2⁴¹, 258, F₂, 8, 8) (dual of [(258, 8), 2023, 9]-NRT-code), using OA 4-folding and stacking based on linear OA(2⁴¹, 1032, F₂, 8) (dual of [1032, 991, 9]-code), using

discarding factors / shortening the dual code based on linear OA(2⁴¹, 1035, F₂, 8) (dual of [1035, 994, 9]-code), using
- 1 times truncation [i] based on linear OA(2⁴², 1036, F₂, 9) (dual of [1036, 994, 10]-code), using
  - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
    1. linear OA(2⁴¹, 1024, F₂, 9) (dual of [1024, 983, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    2. linear OA(2³¹, 1024, F₂, 7) (dual of [1024, 993, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. linear OA(2¹¹, 12, F₂, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,2)), using
      - dual of repetition code with length 12 [i]
    4. linear OA(2¹, 12, F₂, 1) (dual of [12, 11, 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(2²²⁵, 1048833, F₂, 8, 16) (dual of [(1048833, 8), 8390439, 17]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²²⁶, 1048833, F₂, 8, 17) (dual of [(1048833, 8), 8390438, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Digital (33, 41, 258)-net over F₂	[i]	Net Defined by OOA