MinT - Information on Result #2226998

Information on Result #2226998

Linear OA(2²³⁶, 16431, F₂, 32) (dual of [16431, 16195, 33]-code), using 1 times truncation based on linear OA(2²³⁷, 16432, F₂, 33) (dual of [16432, 16195, 34]-code), using

constructionÂ X applied to C_e(32) âŠ‚ C_e(26) [i] based on
1. linear OA(2²²⁵, 16384, F₂, 33) (dual of [16384, 16159, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
2. linear OA(2¹⁸³, 16384, F₂, 27) (dual of [16384, 16201, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
3. linear OA(2¹², 48, F₂, 5) (dual of [48, 36, 6]-code), using
  - adding a parity check bit [i] based on linear OA(2¹¹, 47, F₂, 4) (dual of [47, 36, 5]-code), using
    - extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F₂, using
      - linear code embedding found in a computer search [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(2²³⁶, 8215, F₂, 2, 32) (dual of [(8215, 2), 16194, 33]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2²³⁶, 5477, F₂, 3, 32) (dual of [(5477, 3), 16195, 33]-NRT-code)	[i]
3	Linear OOA(2²³⁶, 4107, F₂, 4, 32) (dual of [(4107, 4), 16192, 33]-NRT-code)	[i]
4	Linear OOA(2²³⁶, 3286, F₂, 5, 32) (dual of [(3286, 5), 16194, 33]-NRT-code)	[i]
5	Linear OOA(2²³⁶, 2738, F₂, 6, 32) (dual of [(2738, 6), 16192, 33]-NRT-code)	[i]
6	Linear OOA(2²³⁶, 2347, F₂, 7, 32) (dual of [(2347, 7), 16193, 33]-NRT-code)	[i]
7	Linear OOA(2²³⁶, 2053, F₂, 8, 32) (dual of [(2053, 8), 16188, 33]-NRT-code)	[i]