Galois LCD codes over finite fields
Copyright policy )Galois LCD codes over finite fields
In this paper, we study the complementary dual codes in more general setting (which are called Galois LCD codes) by a uniform method. A necessary and sufficient condition for linear codes to be Galois LCD codes is determined, and constacyclic codes to be Galois LCD codes are characterized. Some illustrative examples which constacyclic codes are Galois LCD MDS codes are provided as well. In particular, we study Hermitian LCD constacyclic codes. Finally, we present a construction of a class of Hermitian LCD codes which are also MDS codes.
- Central China Normal University China (People's Republic of)
- Hubei Polytechnic University China (People's Republic of)
FOS: Computer and information sciences, Other types of codes, Computer Science - Information Theory, Information Theory (cs.IT), Algebraic coding theory; cryptography (number-theoretic aspects), constacyclic code, \(k\)-Galois LCD code, cyclotomic coset, Cyclic codes, MDS code
FOS: Computer and information sciences, Other types of codes, Computer Science - Information Theory, Information Theory (cs.IT), Algebraic coding theory; cryptography (number-theoretic aspects), constacyclic code, \(k\)-Galois LCD code, cyclotomic coset, Cyclic codes, MDS code
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