MinT - Information on Result #880359

Information on Result #880359

Linear OOA(256⁵⁸, 32779, F₂₅₆, 2, 26) (dual of [(32779, 2), 65500, 27]-NRT-code), using OOA 2-folding based on linear OA(256⁵⁸, 65558, F₂₅₆, 26) (dual of [65558, 65500, 27]-code), using

discarding factors / shortening the dual code based on linear OA(256⁵⁸, 65559, F₂₅₆, 26) (dual of [65559, 65501, 27]-code), using
- constructionÂ X applied to C_e(25) âŠ‚ C_e(17) [i] based on
  1. 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]
  2. linear OA(256³⁵, 65536, F₂₅₆, 18) (dual of [65536, 65501, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
  3. linear OA(256⁷, 23, F₂₅₆, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
    - discarding factors / shortening the dual code based on linear OA(256⁷, 256, F₂₅₆, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
      - Reedâ€“Solomon code RS(249,256) [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(256⁵⁸, 26995, F₂₅₆, 3, 26) (dual of [(26995, 3), 80927, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁵⁸, 26995, F₂₅₆, 4, 26) (dual of [(26995, 4), 107922, 27]-NRT-code)	[i]
3	Linear OOA(256⁵⁸, 26995, F₂₅₆, 5, 26) (dual of [(26995, 5), 134917, 27]-NRT-code)	[i]
4	Linear OOA(256⁵⁸, 26995, F₂₅₆, 6, 26) (dual of [(26995, 6), 161912, 27]-NRT-code)	[i]
5	Digital (32, 58, 26995)-net over F₂₅₆	[i]