MinT - Information on Result #1592432

Information on Result #1592432

Linear OOA(2¹⁵⁸, 1164, F₂, 4, 26) (dual of [(1164, 4), 4498, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁵⁸, 1164, F₂, 3, 26) (dual of [(1164, 3), 3334, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁵⁸, 1369, F₂, 3, 26) (dual of [(1369, 3), 3949, 27]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹⁵⁸, 1369, F₂, 3, 27) (dual of [(1369, 3), 3949, 28]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹⁵⁸, 4107, F₂, 27) (dual of [4107, 3949, 28]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁵⁸, 4109, F₂, 27) (dual of [4109, 3951, 28]-code), using
      - constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
        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(2¹⁴⁵, 4096, F₂, 25) (dual of [4096, 3951, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(2¹⁵⁸, 582, F₂, 8, 26) (dual of [(582, 8), 4498, 27]-NRT-code)	[i]		OOA Folding