MinT - Information on Result #880144

Information on Result #880144

Linear OOA(256⁴⁰, 32776, F₂₅₆, 2, 18) (dual of [(32776, 2), 65512, 19]-NRT-code), using OOA 2-folding based on linear OA(256⁴⁰, 65552, F₂₅₆, 18) (dual of [65552, 65512, 19]-code), using

discarding factors / shortening the dual code based on linear OA(256⁴⁰, 65553, F₂₅₆, 18) (dual of [65553, 65513, 19]-code), using
- constructionÂ X applied to C_e(17) âŠ‚ C_e(11) [i] based on
  1. 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]
  2. 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]
  3. linear OA(256⁵, 17, F₂₅₆, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
    - discarding factors / shortening the dual code based on linear OA(256⁵, 256, F₂₅₆, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
      - Reedâ€“Solomon code RS(251,256) [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(256⁴⁰, 31770, F₂₅₆, 3, 18) (dual of [(31770, 3), 95270, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁴⁰, 31770, F₂₅₆, 4, 18) (dual of [(31770, 4), 127040, 19]-NRT-code)	[i]
3	Linear OOA(256⁴⁰, 31770, F₂₅₆, 5, 18) (dual of [(31770, 5), 158810, 19]-NRT-code)	[i]
4	Linear OOA(256⁴⁰, 31770, F₂₅₆, 6, 18) (dual of [(31770, 6), 190580, 19]-NRT-code)	[i]
5	Digital (22, 40, 31770)-net over F₂₅₆	[i]