MinT - Information on Result #1653191

Information on Result #1653191

Linear OOA(256⁵⁸, 16386, F₂₅₆, 5, 28) (dual of [(16386, 5), 81872, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁵⁸, 16386, F₂₅₆, 4, 28) (dual of [(16386, 4), 65486, 29]-NRT-code), using

256¹ times duplication [i] based on linear OOA(256⁵⁷, 16386, F₂₅₆, 4, 28) (dual of [(16386, 4), 65487, 29]-NRT-code), using
- OOA 4-folding [i] based on linear OA(256⁵⁷, 65544, F₂₅₆, 28) (dual of [65544, 65487, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(24) [i] based on
    1. linear OA(256⁵⁵, 65536, F₂₅₆, 28) (dual of [65536, 65481, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(256⁴⁹, 65536, F₂₅₆, 25) (dual of [65536, 65487, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(256⁵⁸, 5461, F₂₅₆, 35, 28) (dual of [(5461, 35), 191077, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row