MinT - Information on Result #2865606

Information on Result #2865606

Linear OOA(2¹⁶⁹, 6557, F₂, 5, 23) (dual of [(6557, 5), 32616, 24]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁶⁸, 6557, F₂, 5, 23) (dual of [(6557, 5), 32617, 24]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁶⁸, 32785, F₂, 23) (dual of [32785, 32617, 24]-code), using
- 1 times code embedding in larger space [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: Constructive and 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		Method
1	Linear OOA(2¹⁶⁹, 5730, F₂, 6, 23) (dual of [(5730, 6), 34211, 24]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁶⁹, 5730, F₂, 7, 23) (dual of [(5730, 7), 39941, 24]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁹, 5730, F₂, 8, 23) (dual of [(5730, 8), 45671, 24]-NRT-code)	[i]
4	Digital (146, 169, 5730)-net over F₂	[i]