New bounds on the minimum distance of cyclic codes

نویسندگان

چکیده

Two bounds on the minimum distance of cyclic codes are proposed. The first one generalizes Roos bound by embedding given code into a product code. second also uses code, namely non-zero-locator but is not directly related to and it special case bound.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A new bound on the minimum distance of cyclic codes using small-minimum-distance cyclic codes

A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann–Tzeng (HT) bound is formulated explicitly. We show that for many cases our approach improves the HT bound. Furthermore, we refine our bound for several families of cyclic codes. We define syndro...

متن کامل

Decoding of repeated-root cyclic codes up to new bounds on their minimum distance

The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. We generalize these two bounds to the case of repeated-root cyclic codes and present a syndrome-based burst error decoding algorithm with guaranteed decoding radius based on an associated folded cyclic code. Furthermore...

متن کامل

Cyclic LRC codes, binary LRC codes, and upper bounds on the distance of cyclic codes

We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalize the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Trans. Inform. Theory, no. 8, 2014). In this paper we focus on optimal cyclic codes that arise from this construction. We give a characterization...

متن کامل

Classi cation of lower bounds on the minimum distance of cyclic codes

Synopsis: This paper provides a framework of lower bounds on the minimum distance of cyclic codes. Root bounds depends solely on the den-ing set and the length of a cyclic code, and the BCH Bound, the Hartmann-Tzeng Bound, Bound A and several Boston Bounds are sown to belong to this family. Border bounds furthermore depends on the dening set of cyclic subcodes as well. The Schaub Bound, the Sin...

متن کامل

Upper Bounds on the Minimum Distance of Quasi-Cyclic LDPC codes Revisited

In this paper we investigate the minimum code distance of QC LDPC codes [1], [2], [3]. These codes form an important subclass of LDPC codes [4], [5]. These codes also are a subclass of protograph-based LDPC codes [6]. QC LDPC codes can be easily stored as their parity-check matrices can be easily described. Besides such codes have efficient encoding [7] and decoding [8] algorithms. All of these...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Advances in Mathematics of Communications

سال: 2021

ISSN: ['1930-5346', '1930-5338']

DOI: https://doi.org/10.3934/amc.2020038