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Switch codes, first proposed by Wang et al., are codes that are designed to increase the parallelism of data writing and reading processes in network switches. A network switch is required to write $n$ incoming packets and read $k$ outgoing packets while using $m$ memory banks, each able to write and read one packet per time unit. Each set of $n$ packets written to the switch simultaneously is called a generation. The objective is to store the packets in the banks such that every request of $k$ packets, which can belong to previous generations, can be handled by reading at most one packet from every bank. In this paper, we study a new type of switch codes that can simultaneously deliver large packet request and good coding rate. These attractive features are achieved by relaxing the request model to a natural sub-class we call consecutive requests. For this new request model, we define a new type of codes called consecutive switch codes. These codes are studied in both the computational and combinatorial models, corresponding to whether the data can be encoded or not. For binary codes, we also study an intermediate model in which a coded packet is formed by the XOR operations of at most two input packets. We present several code constructions and prove the optimality of one family of these codes by providing the corresponding lower bound. Finally, we introduce a construction of conventional switch codes, which improves upon the best known results for the case $n=k$ . [ABSTRACT FROM AUTHOR]

Historically, LCD cyclic codes were referred to as reversible cyclic codes, which had applications in data storage. Due to a newly discovered application in cryptography, there has been renewed interest in LCD codes. In this paper, we explore two special families of LCD cyclic codes, which are both BCH codes. The dimensions and the minimum distances of these LCD BCH codes are investigated. [ABSTRACT FROM AUTHOR]

Motivated by the study of deletion channels, this paper presents improved bounds on the number of subsequences obtained from a binary string $X$ of length $n$ under $t$ deletions. It is known that the number of subsequences in this setting strongly depends on the number of runs in the string $X$ ; where a run is a maximal substring of the same character. Our improved bounds are obtained by a structural analysis of the family of $r$ -run strings $X$ , an analysis in which we identify the extremal strings with respect to the number of subsequences. Specifically, for every $r$ , we present $r$ -run strings with the minimum (respectively maximum) number of subsequences under any $t$ deletions; we perform an exact analysis of the number of subsequences of these extremal strings; and show that this number can be calculated in polynomial time. [ABSTRACT FROM AUTHOR]

In this paper, we present an algebraic construction of binary codes through rational function fields. We make use of certain multiplicative group of rational functions for our construction. In particular, the point at infinity can be employed in our construction to get codes of length up to $q+1$ , where $q$ is the ground field size. As a result, several new binary constant-weight codes are found and many new binary nonlinear codes are presented. [ABSTRACT FROM PUBLISHER]