MinT - Information on Result #2789974

Information on Result #2789974

Linear OOA(2¹⁹⁸, 2051, F₂, 4, 31) (dual of [(2051, 4), 8006, 32]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁹⁷, 2051, F₂, 4, 31) (dual of [(2051, 4), 8007, 32]-NRT-code), using

OOA 4-folding [i] based on linear OA(2¹⁹⁷, 8204, F₂, 31) (dual of [8204, 8007, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁹⁷, 8206, F₂, 31) (dual of [8206, 8009, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
    1. linear OA(2¹⁹⁶, 8192, F₂, 31) (dual of [8192, 7996, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(2¹⁸³, 8192, F₂, 29) (dual of [8192, 8009, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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(2¹⁹⁸, 1822, F₂, 5, 31) (dual of [(1822, 5), 8912, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁹⁸, 1822, F₂, 6, 31) (dual of [(1822, 6), 10734, 32]-NRT-code)	[i]
3	Linear OOA(2¹⁹⁸, 1822, F₂, 7, 31) (dual of [(1822, 7), 12556, 32]-NRT-code)	[i]
4	Linear OOA(2¹⁹⁸, 1822, F₂, 8, 31) (dual of [(1822, 8), 14378, 32]-NRT-code)	[i]
5	Digital (167, 198, 1822)-net over F₂	[i]