MinT - Information on Result #2228433

Information on Result #2228433

Linear OA(3⁷⁸, 111, F₃, 34) (dual of [111, 33, 35]-code), using 1 times truncation based on linear OA(3⁷⁹, 112, F₃, 35) (dual of [112, 33, 36]-code), using

concatenation of two codes [i] based on
1. linear OA(27¹⁷, 28, F₂₇, 17) (dual of [28, 11, 18]-code or 28-arc in PG(16,27)), using
  - extended Reedâ€“Solomon code RS_e(11,27) [i]
  - the expurgated narrow-sense BCH-code C(I) with length 28Â | 27²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (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(3⁸⁰, 113, F₃, 34) (dual of [113, 33, 35]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(3⁸², 119, F₃, 34) (dual of [119, 37, 35]-code)	[i]	VarÅ¡amovâ€“Edel Lengthening
3	Linear OA(3⁸³, 122, F₃, 34) (dual of [122, 39, 35]-code)	[i]
4	Linear OA(3⁸⁴, 125, F₃, 34) (dual of [125, 41, 35]-code)	[i]
5	Linear OA(3⁸⁰, 114, F₃, 34) (dual of [114, 34, 35]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
6	Linear OA(3⁸¹, 116, F₃, 34) (dual of [116, 35, 35]-code)	[i]
7	Linear OA(3⁸², 118, F₃, 34) (dual of [118, 36, 35]-code)	[i]
8	Linear OOA(3⁷⁸, 55, F₃, 2, 34) (dual of [(55, 2), 32, 35]-NRT-code)	[i]	OOA Folding
9	Linear OOA(3⁷⁸, 37, F₃, 3, 34) (dual of [(37, 3), 33, 35]-NRT-code)	[i]	OOA Folding