MinT - Information on Result #880193

Information on Result #880193

Linear OOA(256⁴⁴, 32776, F₂₅₆, 2, 20) (dual of [(32776, 2), 65508, 21]-NRT-code), using OOA 2-folding based on linear OA(256⁴⁴, 65552, F₂₅₆, 20) (dual of [65552, 65508, 21]-code), using

discarding factors / shortening the dual code based on linear OA(256⁴⁴, 65553, F₂₅₆, 20) (dual of [65553, 65509, 21]-code), using
- constructionÂ X applied to C_e(19) âŠ‚ C_e(13) [i] based on
  1. linear OA(256³⁹, 65536, F₂₅₆, 20) (dual of [65536, 65497, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
  2. linear OA(256²⁷, 65536, F₂₅₆, 14) (dual of [65536, 65509, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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(256⁴⁴, 25064, F₂₅₆, 3, 20) (dual of [(25064, 3), 75148, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁴⁴, 25064, F₂₅₆, 4, 20) (dual of [(25064, 4), 100212, 21]-NRT-code)	[i]
3	Linear OOA(256⁴⁴, 25064, F₂₅₆, 5, 20) (dual of [(25064, 5), 125276, 21]-NRT-code)	[i]
4	Linear OOA(256⁴⁴, 25064, F₂₅₆, 6, 20) (dual of [(25064, 6), 150340, 21]-NRT-code)	[i]
5	Digital (24, 44, 25064)-net over F₂₅₆	[i]