MinT - Information on Result #731633

Information on Result #731633

Linear OA(16⁹⁸, 131088, F₁₆, 24) (dual of [131088, 130990, 25]-code), using trace code based on linear OA(256⁴⁹, 65544, F₂₅₆, 24) (dual of [65544, 65495, 25]-code), using

constructionÂ X applied to C_e(23) âŠ‚ C_e(20) [i] based on
1. linear OA(256⁴⁷, 65536, F₂₅₆, 24) (dual of [65536, 65489, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
2. linear OA(256⁴¹, 65536, F₂₅₆, 21) (dual of [65536, 65495, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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 OA(16⁹⁹, 131089, F₁₆, 24) (dual of [131089, 130990, 25]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(16⁹⁸, 122969, F₁₆, 2, 24) (dual of [(122969, 2), 245840, 25]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Digital (74, 98, 122969)-net over F₁₆	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OA(16⁹⁹, 131090, F₁₆, 24) (dual of [131090, 130991, 25]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OOA(16⁹⁸, 65544, F₁₆, 2, 24) (dual of [(65544, 2), 130990, 25]-NRT-code)	[i]	OOA Folding
6	Linear OOA(16⁹⁸, 10924, F₁₆, 24, 24) (dual of [(10924, 24), 262078, 25]-NRT-code)	[i]	OA Folding and Stacking