A coloring problem on the n-cube
Discrete Applied Mathematics
New bounds on a hypercube coloring problem
Information Processing Letters
Acyclic and k-distance coloring of the grid
Information Processing Letters
On a hypercube coloring problem
Journal of Combinatorial Theory Series A
Introduction to Coding Theory
Acyclic colorings of products of trees
Information Processing Letters
A bound on the chromatic number of the square of a planar graph
Journal of Combinatorial Theory Series B
List-coloring the square of a subcubic graph
Journal of Graph Theory
Optimal Lee-Type Local Structures in Cartesian Products of Cycles and Paths
SIAM Journal on Discrete Mathematics
List-Coloring Squares of Sparse Subcubic Graphs
SIAM Journal on Discrete Mathematics
MDS codes over finite principal ideal rings
Designs, Codes and Cryptography
Discrete Applied Mathematics
The Z4-linearity of Kerdock, Preparata, Goethals, and related codes
IEEE Transactions on Information Theory
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Let C"m be the cycle of length m. We denote the Cartesian product of n copies of C"m by G(n,m):=C"m@?C"m@?...@?C"m. The k-distance chromatic number @g"k(G) of a graph G is @g(G^k) where G^k is the kth power of the graph G=(V,E) in which two distinct vertices are adjacent in G^k if and only if their distance in G is at most k. The k-distance chromatic number of G(n,m) is related to optimal codes over the ring of integers modulo m with minimum Lee distance k+1. In this paper, we consider @g"2(G(n,m)) for n=3 and m=3. In particular, we compute exact values of @g"2(G(3,m)) for 3@?m@?8 and m=4k, and upper bounds for m=3k or m=5k, for any positive integer k. We also show that the maximal size of a code in Z"6^3 with minimum Lee distance 3 is 26.