MinT - Information on Result #1096943

Information on Result #1096943

Linear OOA(2²¹¹, 3279, F₂, 5, 30) (dual of [(3279, 5), 16184, 31]-NRT-code), using OOA 5-folding based on linear OA(2²¹¹, 16395, F₂, 30) (dual of [16395, 16184, 31]-code), using

discarding factors / shortening the dual code based on linear OA(2²¹¹, 16398, F₂, 30) (dual of [16398, 16187, 31]-code), using
- 1 times truncation [i] based on linear OA(2²¹², 16399, F₂, 31) (dual of [16399, 16187, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
    1. linear OA(2²¹¹, 16384, F₂, 31) (dual of [16384, 16173, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(2¹⁹⁷, 16384, F₂, 29) (dual of [16384, 16187, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 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(2²¹¹, 3279, F₂, 6, 30) (dual of [(3279, 6), 19463, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹¹, 3279, F₂, 7, 30) (dual of [(3279, 7), 22742, 31]-NRT-code)	[i]
3	Linear OOA(2²¹¹, 3279, F₂, 8, 30) (dual of [(3279, 8), 26021, 31]-NRT-code)	[i]
4	Digital (181, 211, 3279)-net over F₂	[i]