MinT - Information on Result #1518133

Information on Result #1518133

Linear OOA(2²³⁷, 1062, F₂, 3, 40) (dual of [(1062, 3), 2949, 41]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(2²³⁷, 1062, F₂, 40) (dual of [1062, 825, 41]-code), using

discarding factors / shortening the dual code based on linear OA(2²³⁷, 2097, F₂, 40) (dual of [2097, 1860, 41]-code), using
- 5 times code embedding in larger space [i] based on linear OA(2²³², 2092, F₂, 40) (dual of [2092, 1860, 41]-code), using
  - 1 times truncation [i] based on linear OA(2²³³, 2093, F₂, 41) (dual of [2093, 1860, 42]-code), using
    - constructionÂ X applied to C_e(40) âŠ‚ C_e(34) [i] based on
      1. linear OA(2²²¹, 2048, F₂, 41) (dual of [2048, 1827, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
      2. linear OA(2¹⁸⁸, 2048, F₂, 35) (dual of [2048, 1860, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [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: 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		This result only	Method
1	Linear OOA(2²³⁷, 531, F₂, 5, 40) (dual of [(531, 5), 2418, 41]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²³⁷, 531, F₂, 6, 40) (dual of [(531, 6), 2949, 41]-NRT-code)	[i]		OOA Folding