MinT - Information on Result #880028

Information on Result #880028

Linear OOA(256²⁶, 32773, F₂₅₆, 2, 12) (dual of [(32773, 2), 65520, 13]-NRT-code), using OOA 2-folding based on linear OA(256²⁶, 65546, F₂₅₆, 12) (dual of [65546, 65520, 13]-code), using

discarding factors / shortening the dual code based on linear OA(256²⁶, 65547, F₂₅₆, 12) (dual of [65547, 65521, 13]-code), using
- constructionÂ X applied to C_e(11) âŠ‚ C_e(7) [i] based on
  1. 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]
  2. linear OA(256¹⁵, 65536, F₂₅₆, 8) (dual of [65536, 65521, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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 OOA(256²⁶, 32773, F₂₅₆, 3, 12) (dual of [(32773, 3), 98293, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256²⁶, 32773, F₂₅₆, 4, 12) (dual of [(32773, 4), 131066, 13]-NRT-code)	[i]
3	Linear OOA(256²⁶, 32773, F₂₅₆, 5, 12) (dual of [(32773, 5), 163839, 13]-NRT-code)	[i]
4	Linear OOA(256²⁶, 32773, F₂₅₆, 6, 12) (dual of [(32773, 6), 196612, 13]-NRT-code)	[i]
5	Digital (14, 26, 32773)-net over F₂₅₆	[i]