MinT - Information on Result #946687

Information on Result #946687

Linear OOA(2¹⁵⁹, 1370, F₂, 3, 26) (dual of [(1370, 3), 3951, 27]-NRT-code), using OOA 3-folding based on linear OA(2¹⁵⁹, 4110, F₂, 26) (dual of [4110, 3951, 27]-code), using

2 times code embedding in larger space [i] based on linear OA(2¹⁵⁷, 4108, F₂, 26) (dual of [4108, 3951, 27]-code), using
- 1 times truncation [i] based on linear OA(2¹⁵⁸, 4109, F₂, 27) (dual of [4109, 3951, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
    1. linear OA(2¹⁵⁷, 4096, F₂, 27) (dual of [4096, 3939, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(2¹⁴⁵, 4096, F₂, 25) (dual of [4096, 3951, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 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(2¹⁶⁰, 1370, F₂, 3, 26) (dual of [(1370, 3), 3950, 27]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁶¹, 1370, F₂, 3, 26) (dual of [(1370, 3), 3949, 27]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁵⁹, 1203, F₂, 4, 26) (dual of [(1203, 4), 4653, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹⁵⁹, 1203, F₂, 5, 26) (dual of [(1203, 5), 5856, 27]-NRT-code)	[i]
5	Linear OOA(2¹⁵⁹, 1203, F₂, 6, 26) (dual of [(1203, 6), 7059, 27]-NRT-code)	[i]
6	Linear OOA(2¹⁵⁹, 1203, F₂, 7, 26) (dual of [(1203, 7), 8262, 27]-NRT-code)	[i]
7	Linear OOA(2¹⁵⁹, 1203, F₂, 8, 26) (dual of [(1203, 8), 9465, 27]-NRT-code)	[i]
8	Digital (133, 159, 1203)-net over F₂	[i]