MinT - Information on Result #1095984

Information on Result #1095984

Linear OOA(2¹⁶⁴, 13111, F₂, 5, 20) (dual of [(13111, 5), 65391, 21]-NRT-code), using OOA 5-folding based on linear OA(2¹⁶⁴, 65555, F₂, 20) (dual of [65555, 65391, 21]-code), using

3 times code embedding in larger space [i] based on linear OA(2¹⁶¹, 65552, F₂, 20) (dual of [65552, 65391, 21]-code), using
- 1 times truncation [i] based on linear OA(2¹⁶², 65553, F₂, 21) (dual of [65553, 65391, 22]-code), using
  - constructionÂ X applied to C_e(20) âŠ‚ C_e(18) [i] based on
    1. 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]
    2. linear OA(2¹⁴⁵, 65536, F₂, 19) (dual of [65536, 65391, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(2¹⁶⁵, 13111, F₂, 5, 20) (dual of [(13111, 5), 65390, 21]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁶⁴, 13111, F₂, 6, 20) (dual of [(13111, 6), 78502, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁶⁴, 13111, F₂, 7, 20) (dual of [(13111, 7), 91613, 21]-NRT-code)	[i]
4	Linear OOA(2¹⁶⁴, 13111, F₂, 8, 20) (dual of [(13111, 8), 104724, 21]-NRT-code)	[i]
5	Digital (144, 164, 13111)-net over F₂	[i]