Related papers: Balanced Permutation Codes
The simple permutations in two permutation classes --- the 321-avoiding permutations and the skew-merged permutations --- are enumerated using a uniform method. In both cases, these enumerations were known implicitly, by working backwards…
This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion…
Permutation codes, in the form of rank modulation, have shown promise for applications such as flash memory. One of the metrics recently suggested as appropriate for rank modulation is the Ulam metric, which measures the minimum…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…
In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
Coded caching is a technique that generalizes conventional caching and promises significant reductions in traffic over caching networks. However, the basic coded caching scheme requires that each file hosted in the server be partitioned…
A number of classification problems need to deal with data imbalance between classes. Often it is desired to have a high recall on the minority class while maintaining a high precision on the majority class. In this paper, we review a…
The goal of this paper is to construct systematic error-correcting codes for permutations and multi-permutations in the Kendall's $\tau$-metric. These codes are important in new applications such as rank modulation for flash memories. The…
The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding…
This article presents a methodology that automatically derives a combinatorial specification for a permutation class C, given its basis B of excluded patterns and the set of simple permutations in C, when these sets are both finite. This is…
The increasing interest in using quantum error correcting codes in practical devices has heightened the need for designing quantum error correcting codes that can correct against specialized errors, such as that of amplitude damping errors…
In this paper we describe a class of codes called {\it permutation codes}. This class of codes is a generalization of cyclic codes and quasi-cyclic codes. We also give some examples of optimal permutation codes over binary, ternary, and…
The optimal placement of measurement devices in electrical power systems is commonly modeled through the power dominating set problem. However, in real-world applications, these devices have limited capacities, leading to a capacitated…
Motivated by applications in DNA-based storage, we study explicit encoding and decoding schemes of binary strings satisfying locally balanced constraints, where the $(\ell,\delta)$-locally balanced constraint requires that the weight of any…
We consider replication-based distributed storage systems in which each node stores the same quantum of data and each data bit stored has the same replication factor across the nodes. Such systems are referred to as balanced distributed…
Training on class-imbalanced data usually results in biased models that tend to predict samples into the majority classes, which is a common and notorious problem. From the perspective of energy-based model, we demonstrate that the free…
We propose a stronger formulation of the precedence constraints and the station limits for the simple assembly line balancing problem. The linear relaxation of the improved integer program theoretically dominates all previous formulations…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…