MinT - Information on Result #731701

Information on Result #731701

Linear OA(16¹²⁸, 131096, F₁₆, 31) (dual of [131096, 130968, 32]-code), using trace code based on linear OA(256⁶⁴, 65548, F₂₅₆, 31) (dual of [65548, 65484, 32]-code), using

constructionÂ X applied to C([0,15]) âŠ‚ C([0,13]) [i] based on
1. linear OA(256⁶¹, 65537, F₂₅₆, 31) (dual of [65537, 65476, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
2. linear OA(256⁵³, 65537, F₂₅₆, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [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(16¹²⁹, 131097, F₁₆, 31) (dual of [131097, 130968, 32]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(16¹²⁸, 131096, F₁₆, 2, 31) (dual of [(131096, 2), 262064, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Digital (97, 128, 131096)-net over F₁₆	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OA(16¹²⁹, 131098, F₁₆, 31) (dual of [131098, 130969, 32]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OOA(16¹²⁸, 65548, F₁₆, 2, 31) (dual of [(65548, 2), 130968, 32]-NRT-code)	[i]	OOA Folding