MinT - Information on Result #2259919

Information on Result #2259919

Linear OA(2²⁵³, 16440, F₂, 35) (dual of [16440, 16187, 36]-code), using 1 times code embedding in larger space based on linear OA(2²⁵², 16439, F₂, 35) (dual of [16439, 16187, 36]-code), using

constructionÂ X applied to C_e(34) âŠ‚ C_e(28) [i] based on
1. linear OA(2²³⁹, 16384, F₂, 35) (dual of [16384, 16145, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
2. linear OA(2¹⁹⁷, 16384, F₂, 29) (dual of [16384, 16187, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
3. linear OA(2¹³, 55, F₂, 5) (dual of [55, 42, 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(2²⁵³, 8220, F₂, 2, 35) (dual of [(8220, 2), 16187, 36]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2²⁵³, 5480, F₂, 3, 35) (dual of [(5480, 3), 16187, 36]-NRT-code)	[i]
3	Linear OOA(2²⁵³, 4110, F₂, 4, 35) (dual of [(4110, 4), 16187, 36]-NRT-code)	[i]
4	Linear OOA(2²⁵³, 3288, F₂, 5, 35) (dual of [(3288, 5), 16187, 36]-NRT-code)	[i]
5	Linear OOA(2²⁵³, 2740, F₂, 6, 35) (dual of [(2740, 6), 16187, 36]-NRT-code)	[i]
6	Linear OOA(2²⁵³, 2055, F₂, 8, 35) (dual of [(2055, 8), 16187, 36]-NRT-code)	[i]