MinT - Information on Result #1564524

Information on Result #1564524

Linear OOA(64⁵⁵, 103786, F₆₄, 3, 19) (dual of [(103786, 3), 311303, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64⁵⁵, 103786, F₆₄, 2, 19) (dual of [(103786, 2), 207517, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(64⁵⁵, 131073, F₆₄, 2, 19) (dual of [(131073, 2), 262091, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁵⁵, 262146, F₆₄, 19) (dual of [262146, 262091, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁵⁵, 262147, F₆₄, 19) (dual of [262147, 262092, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
      1. linear OA(64⁵⁵, 262144, F₆₄, 19) (dual of [262144, 262089, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(64⁵², 262144, F₆₄, 18) (dual of [262144, 262092, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(64⁵⁵, 34595, F₆₄, 21, 19) (dual of [(34595, 21), 726440, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row