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Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…
The secure multiplex coding (SMC) is a technique to remove rate loss in the coding for wire-tap channels and broadcast channels with confidential messages caused by the inclusion of random bits into transmitted signals. SMC replaces the…
Maximum distance separable (MDS) codes are very important in both theory and practice. There is a classical construction of a family of $[2^m+1, 2u-1, 2^m-2u+3]$ MDS codes for $1 \leq u \leq 2^{m-1}$, which are cyclic, reversible and BCH…
Let $p$ be an odd prime and $r,s,m$ be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of $2^rp^s$ over the finite field…
The square $C^{*2}$ of a linear error correcting code $C$ is the linear code spanned by the component-wise products of every pair of (non-necessarily distinct) words in $C$. Squares of codes have gained attention for several applications…
Cyclic redundancy check (CRC) codes check if a codeword is correctly received. This paper presents an algorithm to design CRC codes that are optimized for the code-specific error behavior of a specified feedforward convolutional code. The…
We introduce a method for securely delivering a set of messages to a group of clients over a broadcast erasure channel where each client is interested in a distinct message. Each client is able to obtain its own message but not the others'.…
Combinatorial $t$-designs have wide applications in coding theory, cryptography, communications and statistics. It is well known that the supports of all codewords with a fixed weight in a code may give a $t$-design. In this paper, we first…
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…
We propose a two-layer coding architecture for communication of multiple users over a shared slotted medium enabling joint collision resolution and decoding. Each user first encodes its information bits with an outer code for reliability,…
Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are presented. The first…
This paper proposes an erasure correcting code and its systematic form for the distributed storage system. The proposed codes are encoded by exclusive OR and bit-level shift operation. By the shift operation, the encoded packets are…
In this paper, a family of five-weight reducible cyclic codes is presented. Furthermore, the weight distribution of these cyclic codes is determined, which follows from the determination of value distributions of certain exponential sums.
In this paper, new index coding problems are studied, where each receiver has erroneous side information. Although side information is a crucial part of index coding, the existence of erroneous side information has not yet been considered.…
Flag codes that are orbits of a cyclic subgroup of the general linear group acting on flags of a vector space over a finite field, are called cyclic orbit flag codes. In this paper we present a new contribution to the study of such codes…
Variable-length splittable codes are derived from encoding sequences of ordered integer pairs, where one of the pair's components is upper bounded by some constant, and the other one is any positive integer. Each pair is encoded by the…
This letter considers a network comprising a transmitter, which employs random linear network coding to encode a message, a legitimate receiver, which can recover the message if it gathers a sufficient number of linearly independent coded…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
Subspace codes were introduced by K\"otter and Kschischang for error control in random linear network coding. In this paper, a layered type of subspace codes is considered, which can be viewed as a superposition of multiple component…
In the setting of error correcting codes, Alice wants to send a message $x \in \{0,1\}^n$ to Bob via an encoding $\text{enc}(x)$ that is resilient to error. In this work, we investigate the scenario where Bob is a low space decoder. More…