On perfect Lee codes

Discrete Mathematics

Volumn 309, Issue 18, 2009, Pages 5551-5561

  Horak, P ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Golomb Welch conjecture; Perfect Lee code

Indexed keywords

BLOCK LENGTHS; GOLOMB-WELCH CONJECTURE; PERFECT LEE CODE;

EID: 69549084976     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2008.03.019     Document Type: Article

References (21)

1. B.F. Al-Bdaiwi, B. Bose, On resource placements in 3D tori, in: Proc. SCI 2001, vol. 5 July 2001, pp. 96-101
2. Al-Bdaiwi B.F., and Bose B. Quasi-perfect Lee distance codes. IEEE Trans. Inform. Theory 49 June (2003) 1535-1539
3. Al-Bdaiwi B.F., and Horak P. Perfect distance-d placements in 3-dimensional tori. JCMCC 43 (2002) 159-174
4. B.F. Al-Bdaiwi, P. Horak, L. Millazo, Perfect 1-error correcting Lee codes, a manuscript
5. Astola J. On perfect codes in the Lee metric. Ann. Univ. Turku (A) 176 1 (1978) 56
6. Astola J. On perfect Lee-codes over small alphabets of odd cardinality. Discrete Appl. Math. 4 (1982) 227-228
7. Bae M., and Bose B. Resource placement in torus-based networks. IEEE Trans. Comput. 46 10 (1997) 1083-1092
8. Golomb S.W., and Welsh L.R. Algebraic coding and the Lee metric. Error Correcting Codes (1968), Wiley, New York 175-189
9. Gravier S., Mollard M., and Payan Ch. On the existence of three-dimensional tiling in the Lee metric. European J. Combin. 19 (1998) 567-572
10. Gravier S., Mollard M., and Payan Ch. On the existence of three-dimensional tiling in the Lee metric II. Discrete Math. 235 (2001) 151-157
11. P. Horak, Tiling in Lee metric, European J. Combin. (in press)
12. Horak P., and Al-Bdaiwi B.F. Fast decoding quasi-perfect Lee distance codes. Design, Codes, Cryptography 40 (2006) 357-367
13. Huffman W.C., and Pless V. Fundamentals of Error-Correcting Codes (2003), Cambridge University Press, Cambridge
14. Lepisto T. Bounds for perfect Lee codes over small alphabets. Ann. Univ. Turku Ser. A I 186 (1984) 59-63
15. Livingston M., and Stout Q. Perfect dominating sets. Congr. Numer. 79 (1990) 187-203
16. Molnar E. Sui mosaici dello spazio di dimensione n. Atti Della Accademia Nazionale dei Lincei, Rend. Sci. Fis. Mat. Nat. 51 (1971) 177-185
17. Post K.A. Nonexistence theorem on perfect Lee codes over large alphabets. Information and Control 29 (1975) 369-380
18. Quistroff J. New upper bounds on Lee codes. Discrete Appl. Math. 154 (2006) 1510-1521
19. Špacapan S. Non-existence of face-to-face four dimensional tiling in the Lee metric. European J. Combin. 28 (2007) 127-133
20. Szabó S. On mosaics consisting of multidimensional crosses. Acta Math. Acad. Sci. Hung. 38 (1981) 191-203
21. Szabó S. On the problem of regularity of a type on n-dimensional tilings. Discrete Math. 45 (1983) 313-317