MinT - Information on Result #2865327

Information on Result #2865327

Linear OOA(2¹⁷⁴, 26218, F₂, 5, 20) (dual of [(26218, 5), 130916, 21]-NRT-code), using 2² times duplication based on linear OOA(2¹⁷², 26218, F₂, 5, 20) (dual of [(26218, 5), 130918, 21]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁷², 131090, F₂, 20) (dual of [131090, 130918, 21]-code), using
- strength reduction [i] based on linear OA(2¹⁷², 131090, F₂, 21) (dual of [131090, 130918, 22]-code), using
  - constructionÂ X applied to C_e(20) âŠ‚ C_e(18) [i] based on
    1. linear OA(2¹⁷¹, 131072, F₂, 21) (dual of [131072, 130901, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    2. linear OA(2¹⁵⁴, 131072, F₂, 19) (dual of [131072, 130918, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(2¹, 18, F₂, 1) (dual of [18, 17, 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(2¹⁷⁴, 26001, F₂, 6, 20) (dual of [(26001, 6), 155832, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁷⁴, 26001, F₂, 7, 20) (dual of [(26001, 7), 181833, 21]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁴, 26001, F₂, 8, 20) (dual of [(26001, 8), 207834, 21]-NRT-code)	[i]
4	Digital (154, 174, 26001)-net over F₂	[i]