MinT - Information on Result #947039

Information on Result #947039

Linear OOA(2¹⁹⁶, 2748, F₂, 3, 29) (dual of [(2748, 3), 8048, 30]-NRT-code), using OOA 3-folding based on linear OA(2¹⁹⁶, 8244, F₂, 29) (dual of [8244, 8048, 30]-code), using

constructionÂ X applied to C_e(28) âŠ‚ C_e(22) [i] based on
1. 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]
2. linear OA(2¹⁴⁴, 8192, F₂, 23) (dual of [8192, 8048, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
3. linear OA(2¹³, 52, F₂, 5) (dual of [52, 39, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³, 63, F₂, 5) (dual of [63, 50, 6]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(2¹⁹⁶, 2110, F₂, 4, 29) (dual of [(2110, 4), 8244, 30]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁹⁶, 2110, F₂, 5, 29) (dual of [(2110, 5), 10354, 30]-NRT-code)	[i]
3	Linear OOA(2¹⁹⁶, 2110, F₂, 6, 29) (dual of [(2110, 6), 12464, 30]-NRT-code)	[i]
4	Linear OOA(2¹⁹⁶, 2110, F₂, 7, 29) (dual of [(2110, 7), 14574, 30]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁶, 2110, F₂, 8, 29) (dual of [(2110, 8), 16684, 30]-NRT-code)	[i]
6	Digital (167, 196, 2110)-net over F₂	[i]