MinT - Information on Result #2667872

Information on Result #2667872

Linear OOA(2¹⁶², 1371, F₂, 3, 27) (dual of [(1371, 3), 3951, 28]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁵⁹, 1370, F₂, 3, 27) (dual of [(1370, 3), 3951, 28]-NRT-code), using

OOA 3-folding [i] based on linear OA(2¹⁵⁹, 4110, F₂, 27) (dual of [4110, 3951, 28]-code), using
- 1 times code embedding in larger space [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(2¹⁶², 1103, F₂, 4, 27) (dual of [(1103, 4), 4250, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁶², 1103, F₂, 5, 27) (dual of [(1103, 5), 5353, 28]-NRT-code)	[i]
3	Linear OOA(2¹⁶², 1103, F₂, 6, 27) (dual of [(1103, 6), 6456, 28]-NRT-code)	[i]
4	Linear OOA(2¹⁶², 1103, F₂, 7, 27) (dual of [(1103, 7), 7559, 28]-NRT-code)	[i]
5	Linear OOA(2¹⁶², 1103, F₂, 8, 27) (dual of [(1103, 8), 8662, 28]-NRT-code)	[i]
6	Digital (135, 162, 1103)-net over F₂	[i]