MinT - Information on Result #2921411

Information on Result #2921411

Linear OOA(2¹⁸⁵, 174766, F₂, 6, 19) (dual of [(174766, 6), 1048411, 20]-NRT-code), using 2³ times duplication based on linear OOA(2¹⁸², 174766, F₂, 6, 19) (dual of [(174766, 6), 1048414, 20]-NRT-code), using

OOA 6-folding [i] based on linear OA(2¹⁸², 1048596, F₂, 19) (dual of [1048596, 1048414, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁸², 1048597, F₂, 19) (dual of [1048597, 1048415, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
    1. linear OA(2¹⁸¹, 1048576, F₂, 19) (dual of [1048576, 1048395, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(2¹⁶¹, 1048576, F₂, 17) (dual of [1048576, 1048415, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(2¹, 21, F₂, 1) (dual of [21, 20, 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(2¹⁸⁵, 163561, F₂, 7, 19) (dual of [(163561, 7), 1144742, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸⁵, 163561, F₂, 8, 19) (dual of [(163561, 8), 1308303, 20]-NRT-code)	[i]
3	Digital (166, 185, 163561)-net over F₂	[i]