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Gray Codes and Enumerative Coding for Vector Spaces

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1 Author(s)
Schwartz, M. ; Dept. of Electr. & Comput. Eng., Ben-Gurion Univ. of the Negev, Beer-Sheva, Israel

Gray codes for vector spaces are considered in two graphs: the Grassmann graph, and the projective-space graph, both of which have recently found applications in network coding. For the Grassmann graph, constructions of cyclic optimal codes are given for all parameters. As for the projective-space graph, two constructions for specific parameters are provided, as well some nonexistence results. Furthermore, encoding and decoding algorithms are given for the Grassmannian Gray code, which induce an enumerative-coding scheme. The computational complexity of the algorithms is at least as low as known schemes, and for certain parameter ranges, the new scheme outperforms previously known ones.

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Information Theory, IEEE Transactions on  (Volume:60 ,  Issue: 1 )