MinT - Information on Result #1564723

Information on Result #1564723

Linear OOA(64⁶⁶, 131077, F₆₄, 3, 22) (dual of [(131077, 3), 393165, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64⁶⁶, 131077, F₆₄, 2, 22) (dual of [(131077, 2), 262088, 23]-NRT-code), using

OOA 2-folding [i] based on linear OA(64⁶⁶, 262154, F₆₄, 22) (dual of [262154, 262088, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(64⁶⁶, 262155, F₆₄, 22) (dual of [262155, 262089, 23]-code), using
  - constructionÂ X applied to C_e(21) âŠ‚ C_e(18) [i] based on
    1. linear OA(64⁶⁴, 262144, F₆₄, 22) (dual of [262144, 262080, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    2. 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]
    3. linear OA(64², 11, F₆₄, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
      - discarding factors / shortening the dual code based on linear OA(64², 64, F₆₄, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
        Reedâ€“Solomon code RS(62,64) [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(64⁶⁶, 32769, F₆₄, 27, 22) (dual of [(32769, 27), 884697, 23]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row