MinT - Information on Result #2922136

Information on Result #2922136

Linear OOA(2²³⁸, 43694, F₂, 6, 26) (dual of [(43694, 6), 261926, 27]-NRT-code), using 2¹ times duplication based on linear OOA(2²³⁷, 43694, F₂, 6, 26) (dual of [(43694, 6), 261927, 27]-NRT-code), using

OOA 6-folding [i] based on linear OA(2²³⁷, 262164, F₂, 26) (dual of [262164, 261927, 27]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2²³⁵, 262162, F₂, 26) (dual of [262162, 261927, 27]-code), using
  - 1 times truncation [i] based on linear OA(2²³⁶, 262163, F₂, 27) (dual of [262163, 261927, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
      1. linear OA(2²³⁵, 262144, F₂, 27) (dual of [262144, 261909, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      2. linear OA(2²¹⁷, 262144, F₂, 25) (dual of [262144, 261927, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      3. linear OA(2¹, 19, F₂, 1) (dual of [19, 18, 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(2²³⁸, 37552, F₂, 7, 26) (dual of [(37552, 7), 262626, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³⁸, 37552, F₂, 8, 26) (dual of [(37552, 8), 300178, 27]-NRT-code)	[i]
3	Digital (212, 238, 37552)-net over F₂	[i]