کدهای خطی با دوگانگی مکمل
Abstract
1-Introduction
2-Cyclic LCD Codes
3-Cyclic LCD MDS Codes with Length
4-LCD MDS Codes Derived from Cyclic Codes with Length
5-Conclusion
6-Acknowledgement
7-References
Abstract
Linear codes with complementary-duals (LCD) have many applications in cryptography, communication systems and data storage. A q-ary linear code C is called LCD if C∩C⊥ = {۰} holds. Using method of coset theory, we deduce a characterization of LCD cyclic code by its defining set. Then two families of q-ary MDS cyclic LCD codes with lengthes n| (q+1) and n| (q-1) are determined and many new classes of LCD MDS codes are gained.
Introduction
Refs [5-6] first present cyclic LCD codes and [4] constructed LCD MDS codes through Reed-Solomon (RS) codes and presented several methods of constructing LCD codes. Since then, researchers paid much attention to this topic and present many results, such as, LCD cyclic codes in [7-8], a condition that negacyclic codes are LCD codes in [9], LCD MDS codes through GRS codes in [11]. Inspired by [4,9-11], we study the methods of constructing LCD MDS codes from q-ary cyclic codes in this paper. This paper has five parts. In Section 2 we will provide some required basic knowledge on cyclic codes and LCD codes. We derive some classes of LCD codes with length n q ∣( ۱) and new LCD codes from these MDS codes in Section 3. In Section 4, we discuss LCD codes with n q ∣( ۱) . The last Section gives the conclusion.