MinT - Information on Result #2226889

Information on Result #2226889

Linear OA(2²²¹, 8243, F₂, 32) (dual of [8243, 8022, 33]-code), using 1 times truncation based on linear OA(2²²², 8244, F₂, 33) (dual of [8244, 8022, 34]-code), using

constructionÂ X applied to C_e(32) âŠ‚ C_e(26) [i] based on
1. linear OA(2²⁰⁹, 8192, F₂, 33) (dual of [8192, 7983, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
2. linear OA(2¹⁷⁰, 8192, F₂, 27) (dual of [8192, 8022, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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 OA(2²²³, 8245, F₂, 32) (dual of [8245, 8022, 33]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(2²²¹, 4121, F₂, 2, 32) (dual of [(4121, 2), 8021, 33]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2²²¹, 2747, F₂, 3, 32) (dual of [(2747, 3), 8020, 33]-NRT-code)	[i]
4	Linear OOA(2²²¹, 2060, F₂, 4, 32) (dual of [(2060, 4), 8019, 33]-NRT-code)	[i]
5	Linear OOA(2²²¹, 1648, F₂, 5, 32) (dual of [(1648, 5), 8019, 33]-NRT-code)	[i]
6	Linear OOA(2²²¹, 1030, F₂, 8, 32) (dual of [(1030, 8), 8019, 33]-NRT-code)	[i]