MinT - Information on Result #869882

Information on Result #869882

Linear OOA(32⁴⁵, 513, F₃₂, 2, 23) (dual of [(513, 2), 981, 24]-NRT-code), using OOA 2-folding based on linear OA(32⁴⁵, 1026, F₃₂, 23) (dual of [1026, 981, 24]-code), using

constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
1. linear OA(32⁴⁵, 1024, F₃₂, 23) (dual of [1024, 979, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
2. linear OA(32⁴³, 1024, F₃₂, 22) (dual of [1024, 981, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
3. linear OA(32⁰, 2, F₃₂, 0) (dual of [2, 2, 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(32⁵⁶, 546, F₃₂, 2, 23) (dual of [(546, 2), 1036, 24]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(32⁵⁷, 557, F₃₂, 2, 23) (dual of [(557, 2), 1057, 24]-NRT-code)	[i]
3	Linear OOA(32⁵⁹, 577, F₃₂, 2, 23) (dual of [(577, 2), 1095, 24]-NRT-code)	[i]
4	Linear OOA(32⁶¹, 589, F₃₂, 2, 23) (dual of [(589, 2), 1117, 24]-NRT-code)	[i]
5	Linear OOA(32⁶², 590, F₃₂, 2, 23) (dual of [(590, 2), 1118, 24]-NRT-code)	[i]
6	Linear OOA(32⁶³, 611, F₃₂, 2, 23) (dual of [(611, 2), 1159, 24]-NRT-code)	[i]
7	Linear OOA(32⁶⁵, 621, F₃₂, 2, 23) (dual of [(621, 2), 1177, 24]-NRT-code)	[i]
8	Linear OOA(32⁶⁵, 623, F₃₂, 2, 23) (dual of [(623, 2), 1181, 24]-NRT-code)	[i]
9	Digital (22, 45, 452)-net over F₃₂	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound