MinT - Information on Result #1409552

Information on Result #1409552

Linear OOA(3¹¹⁷, 1855, F₃, 2, 23) (dual of [(1855, 2), 3593, 24]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹¹⁷, 1855, F₃, 23) (dual of [1855, 1738, 24]-code), using

discarding factors / shortening the dual code based on linear OA(3¹¹⁷, 2199, F₃, 23) (dual of [2199, 2082, 24]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(3¹¹, 12, F₃, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,3)), using
    - dual of repetition code with length 12 [i]
  2. linear OA(3¹⁰⁶, 2187, F₃, 23) (dual of [2187, 2081, 24]-code), using
    - an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(3¹¹⁷, 927, F₃, 3, 23) (dual of [(927, 3), 2664, 24]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹¹⁷, 927, F₃, 4, 23) (dual of [(927, 4), 3591, 24]-NRT-code)	[i]		OOA Folding