MinT - Information on Result #1603675

Information on Result #1603675

Linear OOA(3¹²³, 59053, F₃, 4, 17) (dual of [(59053, 4), 236089, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹²³, 59053, F₃, 3, 17) (dual of [(59053, 3), 177036, 18]-NRT-code), using

OOA 3-folding [i] based on linear OA(3¹²³, 177159, F₃, 17) (dual of [177159, 177036, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹²², 177158, F₃, 17) (dual of [177158, 177036, 18]-code), using
  - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
    1. linear OA(3¹²², 177147, F₃, 17) (dual of [177147, 177025, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(3¹¹¹, 177147, F₃, 16) (dual of [177147, 177036, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(3⁰, 11, F₃, 0) (dual of [11, 11, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 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(3¹²⁴, 59053, F₃, 4, 17) (dual of [(59053, 4), 236088, 18]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹²⁵, 59053, F₃, 4, 17) (dual of [(59053, 4), 236087, 18]-NRT-code)	[i]		OOA Duplication
3	Linear OOA(3¹²³, 29526, F₃, 20, 17) (dual of [(29526, 20), 590397, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row