MinT - Information on Result #1673265

Information on Result #1673265

Linear OOA(256⁶⁸, 17246, F₂₅₆, 6, 32) (dual of [(17246, 6), 103408, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁶⁸, 17246, F₂₅₆, 3, 32) (dual of [(17246, 3), 51670, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁶⁸, 21851, F₂₅₆, 3, 32) (dual of [(21851, 3), 65485, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(256⁶⁸, 65553, F₂₅₆, 32) (dual of [65553, 65485, 33]-code), using
  - constructionÂ X applied to C_e(31) âŠ‚ C_e(25) [i] based on
    1. linear OA(256⁶³, 65536, F₂₅₆, 32) (dual of [65536, 65473, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
    2. 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]
    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: 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		This result only	Method
1	Linear OOA(256⁶⁸, 5748, F₂₅₆, 42, 32) (dual of [(5748, 42), 241348, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row