MinT - Information on Result #880027

Information on Result #880027

Linear OOA(256²⁵, 32772, F₂₅₆, 2, 12) (dual of [(32772, 2), 65519, 13]-NRT-code), using OOA 2-folding based on linear OA(256²⁵, 65544, F₂₅₆, 12) (dual of [65544, 65519, 13]-code), using

constructionÂ X applied to C_e(11) âŠ‚ C_e(8) [i] based on
1. linear OA(256²³, 65536, F₂₅₆, 12) (dual of [65536, 65513, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
2. linear OA(256¹⁷, 65536, F₂₅₆, 9) (dual of [65536, 65519, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
3. linear OA(256², 8, F₂₅₆, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
  - discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
    - Reedâ€“Solomon code RS(254,256) [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(256³¹, 33029, F₂₅₆, 2, 12) (dual of [(33029, 2), 66027, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(256²⁵, 23203, F₂₅₆, 3, 12) (dual of [(23203, 3), 69584, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(256²⁵, 23203, F₂₅₆, 4, 12) (dual of [(23203, 4), 92787, 13]-NRT-code)	[i]
4	Linear OOA(256²⁵, 23203, F₂₅₆, 5, 12) (dual of [(23203, 5), 115990, 13]-NRT-code)	[i]
5	Linear OOA(256²⁵, 23203, F₂₅₆, 6, 12) (dual of [(23203, 6), 139193, 13]-NRT-code)	[i]
6	Digital (13, 25, 23203)-net over F₂₅₆	[i]