On the Characterization of Linear Uniquely Decodable Codes

نویسندگان

  • Gérard D. Cohen
  • Josep Rifà
  • J. Tena
  • Gilles Zémor
چکیده

A Uniquely Decodable (UD) Code is a code such that any vector of the ambient space has a unique closest codeword. In this paper we begin a study of the structure of UD codes and identify perfect subcodes. In particular we determine all linear UD codes of covering radius ≤ 2.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Local List Recovery of High-Rate Tensor Codes & Applications

In this work, we give the first construction of high-rate locally list-recoverable codes. Listrecovery has been an extremely useful building block in coding theory, and our motivation is to use these codes as such a building block. In particular, our construction gives the first capacity-achieving locally list-decodable codes (over constant-sized alphabet); the first capacity achieving globally...

متن کامل

On the ratio of prefix codes to all uniquely decodable codes with a given length distribution

We investigate the ratio ρn,L of prefix codes to all uniquely decodable codes over an n-letter alphabet and with length distribution L. For any integers n ≥ 2 and m ≥ 1, we construct a lower bound and an upper bound for infL ρn,L, the infimum taken over all sequences L of length m for which the set of uniquely decodable codes with length distribution L is non-empty. As a result, we obtain that ...

متن کامل

Uniquely Decodable Codes and Decoder for Overloaded Synchronous Cdma Systems Field of Invention

A recursive method for constructing uniquely decodable codes for overloaded synchronous CDMA systems, Where large signature codes With groWing overloading factors are reconstructed from the small ones. A class of uniquely decod able signature matrices (or encoders) for overloaded synchro nous CDMA are also devised. A decoder for synchronous CDMA systems to extract the user data by a number of c...

متن کامل

Construction of Uniquely Decodable Codes for the Two-User Binary Adder Channel

A construction of uniquely decodable codes for the two-user binary adder channel is presented. The rates of the codes obtained by this construction are greater than the rates guaranteed by the Coebergh van den Braak and van Tilborg construction and these codes can be used with simple encoding and decoding procedures.

متن کامل

Exponential Lower Bound for 2-Query Locally Decodable Codes

We prove exponential lower bounds on the length of 2-query locally decodable codes. Goldreich et al. recently proved such bounds for the special case of linear locally decodable codes. Our proof shows that a 2-query locally decodable code can be decoded with only 1 quantum query, and then proves an exponential lower bound for such 1-query locally quantum-decodable codes. We also exhibit q-query...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Des. Codes Cryptography

دوره 17  شماره 

صفحات  -

تاریخ انتشار 1999