Dongryul M. Kim

activity

20162026

most cited50 Years of the Golomb--Welch Conjecture

19 citations · 49 across the 29 of their papers we have counts for

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3 papers · 1 filter

math.CO2020★ 1 cited

Connected cubic graphs with the maximum number of perfect matchings

Peter Horak, Dongryul Kim

It is proved that for $n \geq 6$ , the number of perfect matchings in a simple connected cubic graph on $2 n$ vertices is at most $4 f_{n - 1}$ , with $f_{n}$ being the $n$ -th Fibonacci n…

math.CO2017★ 19 cited

Nonexistence of perfect $2$ -error-correcting Lee codes in certain dimensions

Dongryul Kim

The Golomb--Welch conjecture states that there are no perfect $e$ -error-correcting codes in $Z^{n}$ for $n \geq 3$ and $e \geq 2$ . In this note, we prove the nonexistence of p…

math.CO2016★ 3 cited

Algebraic Method in Tilings

Peter Horak, Dongryul Kim

In this paper we introduce a new algebraic method in tilings. Combining this method with Hilbert's Nullstellensatz we obtain a necessary condition for tiling $n$ -space by translate…

Connected cubic graphs with the maximum number of perfect matchings

Nonexistence of perfect 2-error-correcting Lee codes in certain dimensions

Algebraic Method in Tilings

Nonexistence of perfect $2$ -error-correcting Lee codes in certain dimensions