MinT - Information on Result #2226806

Information on Result #2226806

Linear OA(2²⁰⁷, 32815, F₂, 26) (dual of [32815, 32608, 27]-code), using 1 times truncation based on linear OA(2²⁰⁸, 32816, F₂, 27) (dual of [32816, 32608, 28]-code), using

constructionÂ X applied to C_e(26) âŠ‚ C_e(20) [i] based on
1. linear OA(2¹⁹⁶, 32768, F₂, 27) (dual of [32768, 32572, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
2. linear OA(2¹⁵¹, 32768, F₂, 21) (dual of [32768, 32617, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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(2²⁰⁷, 16407, F₂, 2, 26) (dual of [(16407, 2), 32607, 27]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2²⁰⁷, 10938, F₂, 3, 26) (dual of [(10938, 3), 32607, 27]-NRT-code)	[i]
3	Linear OOA(2²⁰⁷, 8203, F₂, 4, 26) (dual of [(8203, 4), 32605, 27]-NRT-code)	[i]
4	Linear OOA(2²⁰⁷, 6563, F₂, 5, 26) (dual of [(6563, 5), 32608, 27]-NRT-code)	[i]
5	Linear OOA(2²⁰⁷, 5469, F₂, 6, 26) (dual of [(5469, 6), 32607, 27]-NRT-code)	[i]
6	Linear OOA(2²⁰⁷, 4687, F₂, 7, 26) (dual of [(4687, 7), 32602, 27]-NRT-code)	[i]
7	Linear OOA(2²⁰⁷, 2524, F₂, 26, 26) (dual of [(2524, 26), 65417, 27]-NRT-code)	[i]	OA Folding and Stacking