MinT - Information on Result #1688429

Information on Result #1688429

Linear OOA(2²⁴³, 1046, F₂, 7, 42) (dual of [(1046, 7), 7079, 43]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴³, 1046, F₂, 2, 42) (dual of [(1046, 2), 1849, 43]-NRT-code), using

OOA 2-folding [i] based on linear OA(2²⁴³, 2092, F₂, 42) (dual of [2092, 1849, 43]-code), using
- 1 times truncation [i] based on linear OA(2²⁴⁴, 2093, F₂, 43) (dual of [2093, 1849, 44]-code), using
  - constructionÂ X applied to C_e(42) âŠ‚ C_e(36) [i] based on
    1. linear OA(2²³², 2048, F₂, 43) (dual of [2048, 1816, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
    2. linear OA(2¹⁹⁹, 2048, F₂, 37) (dual of [2048, 1849, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [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(2²⁴⁴, 1046, F₂, 7, 42) (dual of [(1046, 7), 7078, 43]-NRT-code)	[i]		OOA Duplication