MinT - Information on Result #2788770

Information on Result #2788770

Linear OOA(2¹²², 2052, F₂, 4, 19) (dual of [(2052, 4), 8086, 20]-NRT-code), using 2¹ times duplication based on linear OOA(2¹²¹, 2052, F₂, 4, 19) (dual of [(2052, 4), 8087, 20]-NRT-code), using

OOA 4-folding [i] based on linear OA(2¹²¹, 8208, F₂, 19) (dual of [8208, 8087, 20]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2¹¹⁹, 8206, F₂, 19) (dual of [8206, 8087, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
    1. linear OA(2¹¹⁸, 8192, F₂, 19) (dual of [8192, 8074, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(2¹⁰⁵, 8192, F₂, 17) (dual of [8192, 8087, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(2¹, 14, F₂, 1) (dual of [14, 13, 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(2¹²², 2052, F₂, 5, 19) (dual of [(2052, 5), 10138, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹²², 2052, F₂, 6, 19) (dual of [(2052, 6), 12190, 20]-NRT-code)	[i]
3	Linear OOA(2¹²², 2052, F₂, 7, 19) (dual of [(2052, 7), 14242, 20]-NRT-code)	[i]
4	Linear OOA(2¹²², 2052, F₂, 8, 19) (dual of [(2052, 8), 16294, 20]-NRT-code)	[i]
5	Digital (103, 122, 2052)-net over F₂	[i]