MinT - Information on Result #945153

Information on Result #945153

Linear OOA(2⁷¹, 5466, F₂, 3, 10) (dual of [(5466, 3), 16327, 11]-NRT-code), using OOA 3-folding based on linear OA(2⁷¹, 16398, F₂, 10) (dual of [16398, 16327, 11]-code), using

discarding factors / shortening the dual code based on linear OA(2⁷¹, 16399, F₂, 10) (dual of [16399, 16328, 11]-code), using
- 1 times truncation [i] based on linear OA(2⁷², 16400, F₂, 11) (dual of [16400, 16328, 12]-code), using
  - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
    1. linear OA(2⁷¹, 16384, F₂, 11) (dual of [16384, 16313, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    2. 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]
    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(2⁷¹, 5466, F₂, 4, 10) (dual of [(5466, 4), 21793, 11]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2⁷¹, 5466, F₂, 5, 10) (dual of [(5466, 5), 27259, 11]-NRT-code)	[i]
3	Linear OOA(2⁷¹, 5466, F₂, 6, 10) (dual of [(5466, 6), 32725, 11]-NRT-code)	[i]
4	Linear OOA(2⁷¹, 5466, F₂, 7, 10) (dual of [(5466, 7), 38191, 11]-NRT-code)	[i]
5	Linear OOA(2⁷¹, 5466, F₂, 8, 10) (dual of [(5466, 8), 43657, 11]-NRT-code)	[i]
6	Digital (61, 71, 5466)-net over F₂	[i]