MinT - Information on Result #1673263

Information on Result #1673263

Linear OOA(256⁶⁸, 11602, F₂₅₆, 6, 34) (dual of [(11602, 6), 69544, 35]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁶⁸, 11602, F₂₅₆, 5, 34) (dual of [(11602, 5), 57942, 35]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁶⁸, 13108, F₂₅₆, 5, 34) (dual of [(13108, 5), 65472, 35]-NRT-code), using
- OOA 5-folding [i] based on linear OA(256⁶⁸, 65540, F₂₅₆, 34) (dual of [65540, 65472, 35]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁶⁸, 65541, F₂₅₆, 34) (dual of [65541, 65473, 35]-code), using
    - constructionÂ X applied to C_e(33) âŠ‚ C_e(31) [i] based on
      1. linear OA(256⁶⁷, 65536, F₂₅₆, 34) (dual of [65536, 65469, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
      2. 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]
      3. linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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, 3867, F₂₅₆, 42, 34) (dual of [(3867, 42), 162346, 35]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row