MinT - Information on Result #2480065

Information on Result #2480065

Linear OOA(2¹⁹², 1031, F₂, 2, 35) (dual of [(1031, 2), 1870, 36]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁹¹, 1031, F₂, 2, 35) (dual of [(1031, 2), 1871, 36]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁸⁹, 1030, F₂, 2, 35) (dual of [(1030, 2), 1871, 36]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁸⁹, 2060, F₂, 35) (dual of [2060, 1871, 36]-code), using
  - constructionÂ X applied to C_e(34) âŠ‚ C_e(32) [i] based on
    1. linear OA(2¹⁸⁸, 2048, F₂, 35) (dual of [2048, 1860, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
    2. linear OA(2¹⁷⁷, 2048, F₂, 33) (dual of [2048, 1871, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    3. linear OA(2¹, 12, F₂, 1) (dual of [12, 11, 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(2¹⁹², 738, F₂, 3, 35) (dual of [(738, 3), 2022, 36]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁹², 738, F₂, 4, 35) (dual of [(738, 4), 2760, 36]-NRT-code)	[i]
3	Linear OOA(2¹⁹², 738, F₂, 5, 35) (dual of [(738, 5), 3498, 36]-NRT-code)	[i]
4	Linear OOA(2¹⁹², 738, F₂, 6, 35) (dual of [(738, 6), 4236, 36]-NRT-code)	[i]
5	Linear OOA(2¹⁹², 738, F₂, 7, 35) (dual of [(738, 7), 4974, 36]-NRT-code)	[i]
6	Linear OOA(2¹⁹², 738, F₂, 8, 35) (dual of [(738, 8), 5712, 36]-NRT-code)	[i]
7	Digital (157, 192, 738)-net over F₂	[i]