MinT - Information on Result #946563

Information on Result #946563

Linear OOA(2¹³⁴, 686, F₂, 3, 25) (dual of [(686, 3), 1924, 26]-NRT-code), using OOA 3-folding based on linear OA(2¹³⁴, 2058, F₂, 25) (dual of [2058, 1924, 26]-code), using

discarding factors / shortening the dual code based on linear OA(2¹³⁴, 2060, F₂, 25) (dual of [2060, 1926, 26]-code), using
- constructionÂ X applied to C_e(24) âŠ‚ C_e(22) [i] based on
  1. linear OA(2¹³³, 2048, F₂, 25) (dual of [2048, 1915, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
  2. linear OA(2¹²², 2048, F₂, 23) (dual of [2048, 1926, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(2¹³⁴, 686, F₂, 3, 24) (dual of [(686, 3), 1924, 25]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹³⁴, 625, F₂, 4, 25) (dual of [(625, 4), 2366, 26]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹³⁴, 625, F₂, 5, 25) (dual of [(625, 5), 2991, 26]-NRT-code)	[i]
4	Linear OOA(2¹³⁴, 625, F₂, 6, 25) (dual of [(625, 6), 3616, 26]-NRT-code)	[i]
5	Linear OOA(2¹³⁴, 625, F₂, 7, 25) (dual of [(625, 7), 4241, 26]-NRT-code)	[i]
6	Linear OOA(2¹³⁴, 625, F₂, 8, 25) (dual of [(625, 8), 4866, 26]-NRT-code)	[i]
7	Digital (109, 134, 625)-net over F₂	[i]