MinT - Information on Result #731691

Information on Result #731691

Linear OA(16¹²⁴, 131094, F₁₆, 30) (dual of [131094, 130970, 31]-code), using trace code based on linear OA(256⁶², 65547, F₂₅₆, 30) (dual of [65547, 65485, 31]-code), using

constructionÂ X applied to C_e(29) âŠ‚ C_e(25) [i] based on
1. linear OA(256⁵⁹, 65536, F₂₅₆, 30) (dual of [65536, 65477, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
2. linear OA(256⁵¹, 65536, F₂₅₆, 26) (dual of [65536, 65485, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
3. linear OA(256³, 11, F₂₅₆, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
  - discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
    - Reedâ€“Solomon code RS(253,256) [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(16¹²⁵, 131095, F₁₆, 30) (dual of [131095, 130970, 31]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(16¹²⁴, 131094, F₁₆, 2, 30) (dual of [(131094, 2), 262064, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Digital (94, 124, 131094)-net over F₁₆	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OA(16¹²⁵, 131096, F₁₆, 30) (dual of [131096, 130971, 31]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OOA(16¹²⁴, 65547, F₁₆, 2, 30) (dual of [(65547, 2), 130970, 31]-NRT-code)	[i]	OOA Folding