MinT - Information on Result #1653124

Information on Result #1653124

Linear OOA(256⁵⁴, 16386, F₂₅₆, 5, 26) (dual of [(16386, 5), 81876, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁵⁴, 16386, F₂₅₆, 4, 26) (dual of [(16386, 4), 65490, 27]-NRT-code), using

256¹ times duplication [i] based on linear OOA(256⁵³, 16386, F₂₅₆, 4, 26) (dual of [(16386, 4), 65491, 27]-NRT-code), using
- OOA 4-folding [i] based on linear OA(256⁵³, 65544, F₂₅₆, 26) (dual of [65544, 65491, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(22) [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(256⁴⁵, 65536, F₂₅₆, 23) (dual of [65536, 65491, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    3. linear OA(256², 8, F₂₅₆, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
      - discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
        Reedâ€“Solomon code RS(254,256) [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(256⁵⁴, 5461, F₂₅₆, 35, 26) (dual of [(5461, 35), 191081, 27]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row