MinT - Information on Result #1683286

Information on Result #1683286

Linear OOA(2¹⁷³, 1827, F₂, 7, 27) (dual of [(1827, 7), 12616, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁷³, 1827, F₂, 4, 27) (dual of [(1827, 4), 7135, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁷³, 2052, F₂, 4, 27) (dual of [(2052, 4), 8035, 28]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹⁷³, 8208, F₂, 27) (dual of [8208, 8035, 28]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2¹⁷¹, 8206, F₂, 27) (dual of [8206, 8035, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
      1. linear OA(2¹⁷⁰, 8192, F₂, 27) (dual of [8192, 8022, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      2. linear OA(2¹⁵⁷, 8192, F₂, 25) (dual of [8192, 8035, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      3. linear OA(2¹, 14, F₂, 1) (dual of [14, 13, 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(2¹⁷³, 913, F₂, 35, 27) (dual of [(913, 35), 31782, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row