MinT - Information on Result #1600646

Information on Result #1600646

Linear OOA(2²⁵⁷, 1686, F₂, 4, 40) (dual of [(1686, 4), 6487, 41]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁵⁷, 1686, F₂, 2, 40) (dual of [(1686, 2), 3115, 41]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁵⁷, 2074, F₂, 2, 40) (dual of [(2074, 2), 3891, 41]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2²⁵³, 2072, F₂, 2, 40) (dual of [(2072, 2), 3891, 41]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2²⁵³, 4144, F₂, 40) (dual of [4144, 3891, 41]-code), using
    - strength reduction [i] based on linear OA(2²⁵³, 4144, F₂, 41) (dual of [4144, 3891, 42]-code), using
      - constructionÂ X applied to C_e(40) âŠ‚ C_e(34) [i] based on
        linear OA(2²⁴¹, 4096, F₂, 41) (dual of [4096, 3855, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
        linear OA(2²⁰⁵, 4096, F₂, 35) (dual of [4096, 3891, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
        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(2²⁵⁷, 843, F₂, 7, 40) (dual of [(843, 7), 5644, 41]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁵⁷, 843, F₂, 8, 40) (dual of [(843, 8), 6487, 41]-NRT-code)	[i]		OOA Folding