MinT - Information on Result #1673226

Information on Result #1673226

Linear OOA(256⁶⁶, 14505, F₂₅₆, 6, 32) (dual of [(14505, 6), 86964, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁶⁶, 14505, F₂₅₆, 4, 32) (dual of [(14505, 4), 57954, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁶⁶, 16386, F₂₅₆, 4, 32) (dual of [(16386, 4), 65478, 33]-NRT-code), using
- 256¹ times duplication [i] based on linear OOA(256⁶⁵, 16386, F₂₅₆, 4, 32) (dual of [(16386, 4), 65479, 33]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(256⁶⁵, 65544, F₂₅₆, 32) (dual of [65544, 65479, 33]-code), using
    - constructionÂ X applied to C_e(31) âŠ‚ C_e(28) [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(256⁵⁷, 65536, F₂₅₆, 29) (dual of [65536, 65479, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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(256⁶⁶, 4834, F₂₅₆, 42, 32) (dual of [(4834, 42), 202962, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row