MinT - Information on Result #1700124

Information on Result #1700124

Linear OOA(2¹⁶⁸, 6557, F₂, 8, 22) (dual of [(6557, 8), 52288, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶⁸, 6557, F₂, 5, 22) (dual of [(6557, 5), 32617, 23]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁶⁸, 32785, F₂, 22) (dual of [32785, 32617, 23]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2¹⁶⁶, 32783, F₂, 22) (dual of [32783, 32617, 23]-code), using
  - 1 times truncation [i] based on linear OA(2¹⁶⁷, 32784, F₂, 23) (dual of [32784, 32617, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(20) [i] based on
      1. linear OA(2¹⁶⁶, 32768, F₂, 23) (dual of [32768, 32602, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(2¹⁵¹, 32768, F₂, 21) (dual of [32768, 32617, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 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(2¹⁶⁹, 6557, F₂, 8, 22) (dual of [(6557, 8), 52287, 23]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁷⁰, 6557, F₂, 8, 22) (dual of [(6557, 8), 52286, 23]-NRT-code)	[i]		OOA Duplication