MinT - Information on Result #806420

Information on Result #806420

Linear OOA(2⁹¹, 260, F₂, 2, 20) (dual of [(260, 2), 429, 21]-NRT-code), using OOA 2-folding based on linear OA(2⁹¹, 520, F₂, 20) (dual of [520, 429, 21]-code), using

discarding factors / shortening the dual code based on linear OA(2⁹¹, 521, F₂, 20) (dual of [521, 430, 21]-code), using
- 1 times truncation [i] based on linear OA(2⁹², 522, F₂, 21) (dual of [522, 430, 22]-code), using
  - constructionÂ X applied to C_e(20) âŠ‚ C_e(18) [i] based on
    1. linear OA(2⁹¹, 512, F₂, 21) (dual of [512, 421, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    2. linear OA(2⁸², 512, F₂, 19) (dual of [512, 430, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(2¹, 10, F₂, 1) (dual of [10, 9, 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(2⁹¹, 247, F₂, 3, 20) (dual of [(247, 3), 650, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2⁹¹, 247, F₂, 4, 20) (dual of [(247, 4), 897, 21]-NRT-code)	[i]
3	Linear OOA(2⁹¹, 247, F₂, 5, 20) (dual of [(247, 5), 1144, 21]-NRT-code)	[i]
4	Linear OOA(2⁹¹, 247, F₂, 6, 20) (dual of [(247, 6), 1391, 21]-NRT-code)	[i]
5	Linear OOA(2⁹¹, 247, F₂, 7, 20) (dual of [(247, 7), 1638, 21]-NRT-code)	[i]
6	Linear OOA(2⁹¹, 247, F₂, 8, 20) (dual of [(247, 8), 1885, 21]-NRT-code)	[i]
7	Digital (71, 91, 247)-net over F₂	[i]