Related papers: On the Structure of Interlinked Cycle Structures w…
The question of under what condition some side information for index coding can be removed without affecting the capacity region is studied, which was originally posed by Tahmasbi, Shahrasbi, and Gohari. To answer this question, the notion…
A long-standing conjecture of Thomassen says that every longest cycle of a $3$-connected graph has a chord. Thomassen (2018) proved that if $G$ is $2$-connected and cubic, then any longest cycle must have a chord. He also showed that if $G$…
Locally recoverable (LRC) codes provide a solution to single node failure in distributed storage systems, where it is a very common problem. On the other hand, linear complementary dual (LCD) codes are useful in fault injections attacks on…
The index coding problem is concerned with broadcasting encoded information to a collection of receivers in a way that enables each receiver to discover its required data based on its side information, which comprises the data required by…
In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used to reason about…
The hulls of linear and cyclic codes over finite fields have been of interest and extensively studied due to their wide applications. In this paper, the hulls of cyclic codes of length $n$ over the ring $\mathbb{Z}_4$ have been focused on.…
We study circuit codes with long bit runs (sequences of distinct transitions) and derive a formula for the maximum length for an infinite class of symmetric circuit codes with long bit runs. This formula also results in an improved lower…
In Index coding there is a single sender with multiple messages and multiple receivers each wanting a different set of messages and knowing a different set of messages a priori. The Index Coding problem is to identify the minimum number of…
A class of linear block codes which simultaneously generalizes Gabidulin codes and a class of skew cyclic codes is defined. For these codes, both a Hartmann-Tzeng-like bound and a Roos-like bound, with respect to their rank distance, are…
Cyclic codes are an interesting family of linear codes since they have efficient decoding algorithms and contain optimal codes as subfamilies. Constructing infinite families of cyclic codes with good parameters is important in both theory…
The capacity of symmetric instance of the multiple unicast index coding problem with neighboring antidotes (side-information) with number of messages equal to the number of receivers was given by Maleki, Cadambe and Jafar. In this paper we…
p-Cycles offer ring-like switching speed and mesh-like spare capacity efficiency for protecting network against link failures. This makes them extremely efficient and effective protection technique. p-Cycles can also protect all the links…
This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph…
In this paper, cyclic codes are established over some finite quaternion integer rings with respect to the quaternion Mannheim distance, and de- coding algorithm for these codes is given.
This paper analyzes the distribution of cycle lengths in turbo decoding and low-density parity check (LDPC) graphs. The properties of such cycles are of significant interest in the context of iterative decoding algorithms which are based on…
We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since…
Constacyclic codes over finite fields are a family of linear codes and contain cyclic codes as a subclass. Constacyclic codes are related to many areas of mathematics and outperform cyclic codes in several aspects. Hence, constacyclic codes…
An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding…
A lot of attention has been paid to the investigation of the algebraic properties of linear codes. In most cases, this investigation involves the determination of required code automorphisms, which are useful for decoders, such as the…
Polarization-adjusted convolutional (PAC) codes are a new family of linear block codes that can perform close to the theoretical bounds in the short block-length regime. These codes combine polar coding and convolutional coding. In this…