Name
Abstract | ||
|---|---|---|
For any integer $k \geq 1$, an isometry between codes over $\mathbb{Z}_{2^{k+1}}$ and codes over $\mathbb{Z}_4$ is defined and used to give an equivalent generalization of the Gray map to the one introduced in [C. Carlet, IEEE Trans. Inform. Theory, 44 (1998), pp. 1543-1547]. Several results related to the linearity or nonlinearity of codes over $\mathbb{Z}_{2^{k+1}}$, as well as its corresponding images under this map, are given. These results are similar to those presented in Theorems 4, 5, and 6 of [A. R. Hammons, Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane, and P. Solé, IEEE Trans. Inform. Theory, 40 (1994), pp. 301-319] for codes over $\mathbb{Z}_4$. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1137/S0895480101397219 | SIAM J. Discrete Math. |
Keywords | Field | DocType |
p. v. kumar,gray map,n. j. a,quaternary codes,equivalent generalization,p. sol,c. carlet,ieee trans,corresponding image | Integer,Finite ring,Discrete mathematics,Combinatorics,Gray map,Isometry,Gray code,Coding theory,Linear code,Mathematics | Journal |
Volume | Issue | ISSN |
17 | 1 | 0895-4801 |
Citations | PageRank | References |
5 | 0.45 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| H. Tapia-Recillas | 1 | 12 | 3.88 |
| G. Vega | 2 | 5 | 0.45 |