A class of q-ary linear codes derived from irreducible cyclic codes
نویسندگان
چکیده
Recently, linear codes with a few weights were widely investigated due to their applications in secret sharing schemes and authentication schemes. In this letter, we present a class of q-ary linear codes derived from irreducible cyclic codes with q a prime power. We use Gauss sums to represent its Hamming weights and obtain the bounds of its minimum Hamming distance. In some cases, we explicitly determine its weight distributions which generalize some known results. It is quite interesting that many new codes obtained in this letter are optimal according to some bounds on linear codes.
منابع مشابه
Good Quasi-Cyclic Codes Derived From Irreducible Cyclic Codes
As a generalization of cyclic codes, quasi-cyclic codes contain many good linear codes. Extensive search is made and lots of good quasi-cyclic codes are obtained from irreducible cyclic codes. A new binary [95, 13, 40] code which improves the lower bound on the minimum distance, is also constructed. Index Term — Codes and coding, linear codes, cyclic codes, idempotent, irreducible codes, quasi-...
متن کاملThe Theory of Cyclic Codes and a Generalization to Additive Codes
We present a new approach to the theory of cyclic and constacyclic codes and generalize the theory to cover the family of additive (not necessarily linear) cyclic codes. The approach is based on the action of the Galois group (cyclotomic cosets). The conventional representation of cyclic codes as ideals in a factor ring of the polynomial ring is not needed. 1 General facts on linear codes The c...
متن کاملOptimal locally repairable codes of distance 3 and 4 via cyclic codes
Like classical block codes, a locally repairable code also obeys the Singleton-type bound (we call a locally repairable code optimal if it achieves the Singleton-type bound). In the breakthrough work of [14], several classes of optimal locally repairable codes were constructed via subcodes of Reed-Solomon codes. Thus, the lengths of the codes given in [14] are upper bounded by the code alphabet...
متن کاملXing-Ling codes, duals of their subcodes, and good asymmetric quantum codes
A class of powerful q-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are q-ary block codes that encode k qudits of quantum information into n qudits and correct up to b(dx−1)/2c bit-flip errors and up to b(dz−1)/2c phase-flip errors.. In many cases where the length (q2−q...
متن کاملTwo classes of linear codes with defining sets derived from the kernel of norm or trace
Linear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of q-ary linear codes under some certain conditions, where q is a power of a prime. The lower bound of its minimum Hamming distance is obtained. In some special cases, we evaluate the weight distributions of the linear codes by semi-p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1511.09174 شماره
صفحات -
تاریخ انتشار 2015