Tilings of p-groups are closely associated with error-correcting codes. In [1], M. Dinitz, attempting to generalize full-rank tilings of ?Zn2??to arbitrary finite abelian groups, was able to show that if p ≥5, ...Tilings of p-groups are closely associated with error-correcting codes. In [1], M. Dinitz, attempting to generalize full-rank tilings of ?Zn2??to arbitrary finite abelian groups, was able to show that if p ≥5, then?Znp? admits full-rank tiling and left the case p=3, as an open question. The result proved in this paper the settles of the question for the case p=3.展开更多
The typeⅡ codes have been studied widely in applications since their appearance. With analysis of the algebraic structure of finite field of order 4 （i.e., GF（4））, some necessary and sufficient conditions that a ...The typeⅡ codes have been studied widely in applications since their appearance. With analysis of the algebraic structure of finite field of order 4 （i.e., GF（4））, some necessary and sufficient conditions that a generalized H-code （i.e., GH-code） is a type Ⅱ code over GF（4） are given in this article, and an efficient and simple method to generate type Ⅱ codes from GH-codes over GF（4） is shown. The conclusions further extend the coding theory of type Ⅱ.展开更多
In this paper,the quantum error-correcting codes are generalized to the inhomogenous quantumstate space Cq1 Cq2 ··· Cqn,where qi(1 i n) are arbitrary positive integers.By attaching an abelian group Ai ...In this paper,the quantum error-correcting codes are generalized to the inhomogenous quantumstate space Cq1 Cq2 ··· Cqn,where qi(1 i n) are arbitrary positive integers.By attaching an abelian group Ai of order qi to the space Cqi(1 i n),we present the stabilizer construction of such inhomogenous quantum codes,called additive quantum codes,in term of the character theory of the abelian group A = A1⊕A2⊕···⊕An.As usual case,such construction opens a way to get inhomogenous quantum codes from the classical mixed linear codes.We also present Singleton bound for inhomogenous additive quantum codes and show several quantum codes to meet such bound by using classical mixed algebraic-geometric codes.展开更多
文摘Tilings of p-groups are closely associated with error-correcting codes. In [1], M. Dinitz, attempting to generalize full-rank tilings of ?Zn2??to arbitrary finite abelian groups, was able to show that if p ≥5, then?Znp? admits full-rank tiling and left the case p=3, as an open question. The result proved in this paper the settles of the question for the case p=3.
基金the National Natural Science Foundation of China (60743007)Fujian Province Young Talent Program (2006F3044)+2 种基金Province Natural Science Foundation of Fujian (JA04169)Province Education Department Foundation of Fujian (JB05331)Beijing Municipal Commission of Education Disciplines and Graduate Education Projects (XK100130648)
文摘The typeⅡ codes have been studied widely in applications since their appearance. With analysis of the algebraic structure of finite field of order 4 （i.e., GF（4））, some necessary and sufficient conditions that a generalized H-code （i.e., GH-code） is a type Ⅱ code over GF（4） are given in this article, and an efficient and simple method to generate type Ⅱ codes from GH-codes over GF（4） is shown. The conclusions further extend the coding theory of type Ⅱ.
基金supported by National Natural Science Foundation of China (Grant No.10990011)
文摘In this paper,the quantum error-correcting codes are generalized to the inhomogenous quantumstate space Cq1 Cq2 ··· Cqn,where qi(1 i n) are arbitrary positive integers.By attaching an abelian group Ai of order qi to the space Cqi(1 i n),we present the stabilizer construction of such inhomogenous quantum codes,called additive quantum codes,in term of the character theory of the abelian group A = A1⊕A2⊕···⊕An.As usual case,such construction opens a way to get inhomogenous quantum codes from the classical mixed linear codes.We also present Singleton bound for inhomogenous additive quantum codes and show several quantum codes to meet such bound by using classical mixed algebraic-geometric codes.
