MinT - Information on Result #1565170

Information on Result #1565170

Linear OOA(64⁸⁵, 97674, F₆₄, 3, 29) (dual of [(97674, 3), 292937, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64⁸⁵, 97674, F₆₄, 2, 29) (dual of [(97674, 2), 195263, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(64⁸⁵, 131073, F₆₄, 2, 29) (dual of [(131073, 2), 262061, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁸⁵, 262146, F₆₄, 29) (dual of [262146, 262061, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁸⁵, 262147, F₆₄, 29) (dual of [262147, 262062, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
      1. linear OA(64⁸⁵, 262144, F₆₄, 29) (dual of [262144, 262059, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(64⁸², 262144, F₆₄, 28) (dual of [262144, 262062, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [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(64⁸⁵, 19534, F₆₄, 33, 29) (dual of [(19534, 33), 644537, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row