MinT - Information on Result #1593259

Information on Result #1593259

Linear OOA(2¹⁷², 1067, F₂, 4, 29) (dual of [(1067, 4), 4096, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁷², 1067, F₂, 3, 29) (dual of [(1067, 3), 3029, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁷², 1370, F₂, 3, 29) (dual of [(1370, 3), 3938, 30]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2¹⁷¹, 1370, F₂, 3, 29) (dual of [(1370, 3), 3939, 30]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹⁷¹, 4110, F₂, 29) (dual of [4110, 3939, 30]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(2¹⁷⁰, 4109, F₂, 29) (dual of [4109, 3939, 30]-code), using
      - constructionÂ X applied to C_e(28) âŠ‚ C_e(26) [i] based on
        linear OA(2¹⁶⁹, 4096, F₂, 29) (dual of [4096, 3927, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(2¹⁵⁷, 4096, F₂, 27) (dual of [4096, 3939, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        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(2¹⁷², 533, F₂, 8, 29) (dual of [(533, 8), 4092, 30]-NRT-code)	[i]		OOA Folding