MinT - Information on Result #1564354

Information on Result #1564354

Linear OOA(64⁴⁴, 1956, F₆₄, 3, 21) (dual of [(1956, 3), 5824, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64⁴⁴, 1956, F₆₄, 2, 21) (dual of [(1956, 2), 3868, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(64⁴⁴, 2054, F₆₄, 2, 21) (dual of [(2054, 2), 4064, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁴⁴, 4108, F₆₄, 21) (dual of [4108, 4064, 22]-code), using
  - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
    1. linear OA(64⁴¹, 4097, F₆₄, 21) (dual of [4097, 4056, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    2. linear OA(64³³, 4097, F₆₄, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    3. linear OA(64³, 11, F₆₄, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
      - discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
        Reedâ€“Solomon code RS(61,64) [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(64⁴⁴, 488, F₆₄, 27, 21) (dual of [(488, 27), 13132, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row