MinT - Information on Result #1095892

Information on Result #1095892

Linear OOA(2¹⁵², 13115, F₂, 5, 19) (dual of [(13115, 5), 65423, 20]-NRT-code), using OOA 5-folding based on linear OA(2¹⁵², 65575, F₂, 19) (dual of [65575, 65423, 20]-code), using

constructionÂ X applied to C_e(18) âŠ‚ C_e(14) [i] based on
1. linear OA(2¹⁴⁵, 65536, F₂, 19) (dual of [65536, 65391, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
2. linear OA(2¹¹³, 65536, F₂, 15) (dual of [65536, 65423, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
3. linear OA(2⁷, 39, F₂, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
  - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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(2¹⁵³, 13115, F₂, 5, 19) (dual of [(13115, 5), 65422, 20]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁵², 13115, F₂, 6, 19) (dual of [(13115, 6), 78538, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁵², 13115, F₂, 7, 19) (dual of [(13115, 7), 91653, 20]-NRT-code)	[i]
4	Linear OOA(2¹⁵², 13115, F₂, 8, 19) (dual of [(13115, 8), 104768, 20]-NRT-code)	[i]
5	Digital (133, 152, 13115)-net over F₂	[i]