MinT - Information on Result #2228195

Information on Result #2228195

Linear OA(3⁶⁶, 111, F₃, 26) (dual of [111, 45, 27]-code), using 1 times truncation based on linear OA(3⁶⁷, 112, F₃, 27) (dual of [112, 45, 28]-code), using

concatenation of two codes [i] based on
1. linear OA(27¹³, 28, F₂₇, 13) (dual of [28, 15, 14]-code or 28-arc in PG(12,27)), using
  - extended Reedâ€“Solomon code RS_e(15,27) [i]
  - the expurgated narrow-sense BCH-code C(I) with length 28Â | 27²âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
2. linear OA(3¹, 4, F₃, 1) (dual of [4, 3, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]

Mode: Constructive and 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(3⁶⁸, 113, F₃, 26) (dual of [113, 45, 27]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(3⁶⁹, 114, F₃, 26) (dual of [114, 45, 27]-code)	[i]
3	Linear OA(3⁷⁰, 115, F₃, 26) (dual of [115, 45, 27]-code)	[i]
4	Linear OA(3⁶⁷, 113, F₃, 26) (dual of [113, 46, 27]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OOA(3⁶⁶, 55, F₃, 2, 26) (dual of [(55, 2), 44, 27]-NRT-code)	[i]	OOA Folding
6	Linear OOA(3⁶⁶, 37, F₃, 3, 26) (dual of [(37, 3), 45, 27]-NRT-code)	[i]	OOA Folding