MinT - Information on Result #2226830

Information on Result #2226830

Linear OA(2²²¹, 2092, F₂, 38) (dual of [2092, 1871, 39]-code), using 1 times truncation based on linear OA(2²²², 2093, F₂, 39) (dual of [2093, 1871, 40]-code), using

constructionÂ X applied to C_e(38) âŠ‚ C_e(32) [i] based on
1. linear OA(2²¹⁰, 2048, F₂, 39) (dual of [2048, 1838, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
2. linear OA(2¹⁷⁷, 2048, F₂, 33) (dual of [2048, 1871, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
3. linear OA(2¹², 45, F₂, 5) (dual of [45, 33, 6]-code), using
  - discarding factors / shortening the dual code based on 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 OA(2²²⁴, 2095, F₂, 38) (dual of [2095, 1871, 39]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²²⁵, 2096, F₂, 38) (dual of [2096, 1871, 39]-code)	[i]
3	Linear OA(2²²⁶, 2097, F₂, 38) (dual of [2097, 1871, 39]-code)	[i]
4	Linear OA(2²²⁷, 2098, F₂, 38) (dual of [2098, 1871, 39]-code)	[i]
5	Linear OOA(2²²¹, 1046, F₂, 2, 38) (dual of [(1046, 2), 1871, 39]-NRT-code)	[i]	OOA Folding
6	Linear OOA(2²²¹, 697, F₂, 3, 38) (dual of [(697, 3), 1870, 39]-NRT-code)	[i]
7	Linear OOA(2²²¹, 523, F₂, 4, 38) (dual of [(523, 4), 1871, 39]-NRT-code)	[i]
8	Linear OOA(2²²¹, 418, F₂, 5, 38) (dual of [(418, 5), 1869, 39]-NRT-code)	[i]
9	Linear OOA(2²²¹, 348, F₂, 6, 38) (dual of [(348, 6), 1867, 39]-NRT-code)	[i]
10	Linear OOA(2²²¹, 298, F₂, 7, 38) (dual of [(298, 7), 1865, 39]-NRT-code)	[i]
11	Linear OOA(2²²¹, 261, F₂, 8, 38) (dual of [(261, 8), 1867, 39]-NRT-code)	[i]