MinT - Information on Result #2480066

Information on Result #2480066

Linear OOA(2¹⁹³, 1032, F₂, 2, 35) (dual of [(1032, 2), 1871, 36]-NRT-code), using 2 times NRT-code embedding in larger space 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(2¹⁹³, 756, F₂, 3, 35) (dual of [(756, 3), 2075, 36]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁹³, 756, F₂, 4, 35) (dual of [(756, 4), 2831, 36]-NRT-code)	[i]
3	Linear OOA(2¹⁹³, 756, F₂, 5, 35) (dual of [(756, 5), 3587, 36]-NRT-code)	[i]
4	Linear OOA(2¹⁹³, 756, F₂, 6, 35) (dual of [(756, 6), 4343, 36]-NRT-code)	[i]
5	Linear OOA(2¹⁹³, 756, F₂, 7, 35) (dual of [(756, 7), 5099, 36]-NRT-code)	[i]
6	Linear OOA(2¹⁹³, 756, F₂, 8, 35) (dual of [(756, 8), 5855, 36]-NRT-code)	[i]
7	Digital (158, 193, 756)-net over F₂	[i]