MinT - Information on Result #1600432

Information on Result #1600432

Linear OOA(2²⁵⁵, 1301, F₂, 4, 43) (dual of [(1301, 4), 4949, 44]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁵⁵, 1301, F₂, 3, 43) (dual of [(1301, 3), 3648, 44]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁵⁵, 1370, F₂, 3, 43) (dual of [(1370, 3), 3855, 44]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2²⁵⁵, 4110, F₂, 43) (dual of [4110, 3855, 44]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(2²⁵⁴, 4109, F₂, 43) (dual of [4109, 3855, 44]-code), using
    - constructionÂ X applied to C_e(42) âŠ‚ C_e(40) [i] based on
      1. linear OA(2²⁵³, 4096, F₂, 43) (dual of [4096, 3843, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
      2. 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]
      3. linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(2²⁵⁵, 650, F₂, 7, 43) (dual of [(650, 7), 4295, 44]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁵⁵, 650, F₂, 8, 43) (dual of [(650, 8), 4945, 44]-NRT-code)	[i]		OOA Folding