MinT - Information on Result #2842668

Information on Result #2842668

Linear OOA(2¹⁷⁸, 13110, F₂, 5, 22) (dual of [(13110, 5), 65372, 23]-NRT-code), using strength reduction based on linear OOA(2¹⁷⁸, 13110, F₂, 5, 23) (dual of [(13110, 5), 65372, 24]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁷⁸, 65550, F₂, 23) (dual of [65550, 65372, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁷⁸, 65553, F₂, 23) (dual of [65553, 65375, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(20) [i] based on
    1. linear OA(2¹⁷⁷, 65536, F₂, 23) (dual of [65536, 65359, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. 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]
    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(2¹⁷⁸, 12207, F₂, 6, 22) (dual of [(12207, 6), 73064, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁷⁸, 12207, F₂, 7, 22) (dual of [(12207, 7), 85271, 23]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁸, 12207, F₂, 8, 22) (dual of [(12207, 8), 97478, 23]-NRT-code)	[i]
4	Digital (156, 178, 12207)-net over F₂	[i]