MinT - Information on Result #1164089

Information on Result #1164089

Linear OOA(2⁵⁷, 4099, F₂, 8, 8) (dual of [(4099, 8), 32735, 9]-NRT-code), using OA 4-folding and stacking based on linear OA(2⁵⁷, 16396, F₂, 8) (dual of [16396, 16339, 9]-code), using

discarding factors / shortening the dual code based on linear OA(2⁵⁷, 16399, F₂, 8) (dual of [16399, 16342, 9]-code), using
- 1 times truncation [i] based on linear OA(2⁵⁸, 16400, F₂, 9) (dual of [16400, 16342, 10]-code), using
  - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
    1. linear OA(2⁵⁷, 16384, F₂, 9) (dual of [16384, 16327, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    2. linear OA(2⁴³, 16384, F₂, 7) (dual of [16384, 16341, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. linear OA(2¹⁵, 16, F₂, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
      - dual of repetition code with length 16 [i]
    4. linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 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(2²⁴¹, 1052674, F₂, 8, 16) (dual of [(1052674, 8), 8421151, 17]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²⁴², 1052674, F₂, 8, 17) (dual of [(1052674, 8), 8421150, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Digital (49, 57, 4099)-net over F₂	[i]	Net Defined by OOA