MinT - Information on Result #2841853

Information on Result #2841853

Linear OOA(2¹⁶⁴, 52432, F₂, 5, 18) (dual of [(52432, 5), 261996, 19]-NRT-code), using strength reduction based on linear OOA(2¹⁶⁴, 52432, F₂, 5, 19) (dual of [(52432, 5), 261996, 20]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁶⁴, 262160, F₂, 19) (dual of [262160, 261996, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁶⁴, 262163, F₂, 19) (dual of [262163, 261999, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
    1. linear OA(2¹⁶³, 262144, F₂, 19) (dual of [262144, 261981, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(2¹⁴⁵, 262144, F₂, 17) (dual of [262144, 261999, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(2¹, 19, F₂, 1) (dual of [19, 18, 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(2¹⁶⁴, 51507, F₂, 6, 18) (dual of [(51507, 6), 308878, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁶⁴, 51507, F₂, 7, 18) (dual of [(51507, 7), 360385, 19]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁴, 51507, F₂, 8, 18) (dual of [(51507, 8), 411892, 19]-NRT-code)	[i]
4	Digital (146, 164, 51507)-net over F₂	[i]