MinT - Information on Result #869904

Information on Result #869904

Linear OOA(32⁶⁷, 16385, F₃₂, 2, 23) (dual of [(16385, 2), 32703, 24]-NRT-code), using OOA 2-folding based on linear OA(32⁶⁷, 32770, F₃₂, 23) (dual of [32770, 32703, 24]-code), using

discarding factors / shortening the dual code based on linear OA(32⁶⁷, 32771, F₃₂, 23) (dual of [32771, 32704, 24]-code), using
- constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
  1. linear OA(32⁶⁷, 32768, F₃₂, 23) (dual of [32768, 32701, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  2. linear OA(32⁶⁴, 32768, F₃₂, 22) (dual of [32768, 32704, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
  3. linear OA(32⁰, 3, F₃₂, 0) (dual of [3, 3, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [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(32⁷⁸, 16418, F₃₂, 2, 23) (dual of [(16418, 2), 32758, 24]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(32⁷⁹, 16429, F₃₂, 2, 23) (dual of [(16429, 2), 32779, 24]-NRT-code)	[i]
3	Linear OOA(32⁸¹, 16449, F₃₂, 2, 23) (dual of [(16449, 2), 32817, 24]-NRT-code)	[i]
4	Linear OOA(32⁸³, 16461, F₃₂, 2, 23) (dual of [(16461, 2), 32839, 24]-NRT-code)	[i]
5	Linear OOA(32⁸⁴, 16462, F₃₂, 2, 23) (dual of [(16462, 2), 32840, 24]-NRT-code)	[i]
6	Linear OOA(32⁸⁵, 16483, F₃₂, 2, 23) (dual of [(16483, 2), 32881, 24]-NRT-code)	[i]
7	Linear OOA(32⁸⁷, 16493, F₃₂, 2, 23) (dual of [(16493, 2), 32899, 24]-NRT-code)	[i]
8	Linear OOA(32⁸⁷, 16495, F₃₂, 2, 23) (dual of [(16495, 2), 32903, 24]-NRT-code)	[i]
9	Digital (44, 67, 16385)-net over F₃₂	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound