MinT - Information on Result #1653311

Information on Result #1653311

Linear OOA(256⁶⁵, 28309, F₂₅₆, 5, 29) (dual of [(28309, 5), 141480, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁶⁵, 28309, F₂₅₆, 2, 29) (dual of [(28309, 2), 56553, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁶⁵, 32781, F₂₅₆, 2, 29) (dual of [(32781, 2), 65497, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256⁶⁵, 65562, F₂₅₆, 29) (dual of [65562, 65497, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(19) [i] based on
    1. 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]
    2. linear OA(256³⁹, 65536, F₂₅₆, 20) (dual of [65536, 65497, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    3. linear OA(256⁸, 26, F₂₅₆, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
      - discarding factors / shortening the dual code based on linear OA(256⁸, 256, F₂₅₆, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
        Reedâ€“Solomon code RS(248,256) [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(256⁶⁵, 9436, F₂₅₆, 35, 29) (dual of [(9436, 35), 330195, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row