MinT - Information on Result #2762621

Information on Result #2762621

Linear OOA(2¹⁷¹, 2051, F₂, 4, 26) (dual of [(2051, 4), 8033, 27]-NRT-code), using strength reduction based on linear OOA(2¹⁷¹, 2051, F₂, 4, 27) (dual of [(2051, 4), 8033, 28]-NRT-code), using

OOA 4-folding [i] based on linear OA(2¹⁷¹, 8204, F₂, 27) (dual of [8204, 8033, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁷¹, 8206, F₂, 27) (dual of [8206, 8035, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
    1. linear OA(2¹⁷⁰, 8192, F₂, 27) (dual of [8192, 8022, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(2¹⁵⁷, 8192, F₂, 25) (dual of [8192, 8035, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(2¹, 14, F₂, 1) (dual of [14, 13, 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(2¹⁷¹, 2051, F₂, 5, 26) (dual of [(2051, 5), 10084, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁷¹, 2051, F₂, 6, 26) (dual of [(2051, 6), 12135, 27]-NRT-code)	[i]
3	Linear OOA(2¹⁷¹, 2051, F₂, 7, 26) (dual of [(2051, 7), 14186, 27]-NRT-code)	[i]
4	Linear OOA(2¹⁷¹, 2051, F₂, 8, 26) (dual of [(2051, 8), 16237, 27]-NRT-code)	[i]
5	Digital (145, 171, 2051)-net over F₂	[i]