MinT - Information on Result #1652922

Information on Result #1652922

Linear OOA(256⁴⁰, 15164, F₂₅₆, 5, 20) (dual of [(15164, 5), 75780, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁴⁰, 15164, F₂₅₆, 4, 20) (dual of [(15164, 4), 60616, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁴⁰, 16385, F₂₅₆, 4, 20) (dual of [(16385, 4), 65500, 21]-NRT-code), using
- OOA 4-folding [i] based on linear OA(256⁴⁰, 65540, F₂₅₆, 20) (dual of [65540, 65500, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁴⁰, 65541, F₂₅₆, 20) (dual of [65541, 65501, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(17) [i] based on
      1. 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]
      2. linear OA(256³⁵, 65536, F₂₅₆, 18) (dual of [65536, 65501, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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(256⁴⁰, 7581, F₂₅₆, 25, 20) (dual of [(7581, 25), 189485, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row