MinT - Information on Result #870865

Information on Result #870865

Linear OOA(32⁶⁸, 513, F₃₂, 2, 36) (dual of [(513, 2), 958, 37]-NRT-code), using OOA 2-folding based on linear OA(32⁶⁸, 1026, F₃₂, 36) (dual of [1026, 958, 37]-code), using

constructionÂ X applied to C_e(35) âŠ‚ C_e(34) [i] based on
1. linear OA(32⁶⁸, 1024, F₃₂, 36) (dual of [1024, 956, 37]-code), using an extension C_e(35) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,35], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]
2. linear OA(32⁶⁶, 1024, F₃₂, 35) (dual of [1024, 958, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [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(32⁸⁶, 546, F₃₂, 2, 36) (dual of [(546, 2), 1006, 37]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(32⁸⁷, 557, F₃₂, 2, 36) (dual of [(557, 2), 1027, 37]-NRT-code)	[i]
3	Linear OOA(32⁸⁹, 577, F₃₂, 2, 36) (dual of [(577, 2), 1065, 37]-NRT-code)	[i]
4	Linear OOA(32⁹¹, 589, F₃₂, 2, 36) (dual of [(589, 2), 1087, 37]-NRT-code)	[i]
5	Linear OOA(32⁹³, 611, F₃₂, 2, 36) (dual of [(611, 2), 1129, 37]-NRT-code)	[i]
6	Linear OOA(32⁹⁵, 617, F₃₂, 2, 36) (dual of [(617, 2), 1139, 37]-NRT-code)	[i]
7	Linear OOA(32⁹⁷, 633, F₃₂, 2, 36) (dual of [(633, 2), 1169, 37]-NRT-code)	[i]
8	Linear OOA(32¹⁰¹, 641, F₃₂, 2, 36) (dual of [(641, 2), 1181, 37]-NRT-code)	[i]
9	Digital (32, 68, 419)-net over F₃₂	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound