MinT - Information on Result #1096569

Information on Result #1096569

Linear OOA(2¹⁸³, 3279, F₂, 5, 26) (dual of [(3279, 5), 16212, 27]-NRT-code), using OOA 5-folding based on linear OA(2¹⁸³, 16395, F₂, 26) (dual of [16395, 16212, 27]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁸³, 16398, F₂, 26) (dual of [16398, 16215, 27]-code), using
- 1 times truncation [i] based on linear OA(2¹⁸⁴, 16399, F₂, 27) (dual of [16399, 16215, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
    1. linear OA(2¹⁸³, 16384, F₂, 27) (dual of [16384, 16201, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(2¹⁶⁹, 16384, F₂, 25) (dual of [16384, 16215, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(2¹⁸³, 3279, F₂, 6, 26) (dual of [(3279, 6), 19491, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸³, 3279, F₂, 7, 26) (dual of [(3279, 7), 22770, 27]-NRT-code)	[i]
3	Linear OOA(2¹⁸³, 3279, F₂, 8, 26) (dual of [(3279, 8), 26049, 27]-NRT-code)	[i]
4	Digital (157, 183, 3279)-net over F₂	[i]