Related papers: Codes induced by alternative codes
Hybrid codes simultaneously encode both quantum and classical information into physical qubits. We give several general results about hybrid codes, most notably that the quantum codes comprising a genuine hybrid code must be impure and that…
In a recent paper, we defined twisted unitary $1$-groups and showed that they automatically induced error-detecting quantum codes. We also showed that twisted unitary $1$-groups correspond to irreducible products of characters thereby…
Lossless variable-length source coding with codeword cost is considered for general sources. The problem setting, where we impose on unequal costs on code symbols, is called the variable-length coding with codeword cost. In this problem,…
Computer algorithms are written with the intent that when run they perform a useful function. Typically any information obtained is unknown until the algorithm is run. However, if the behavior of an algorithm can be fully described by…
Network coding is studied when an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than when the adversary controls a given number of edges in the…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
A novel implementation of a special class of Galois ring, in which the multiplication can be realized by a cyclic convolution, is applied to the construction of network codes. The primitive operations involved are byte-wise shifts and…
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…
This paper investigates the application of the theoretical algebraic notion of a separable ring extension, in the realm of cyclic convolutional codes or, more generally, ideal codes. We work under very mild conditions, that cover all…
Auxiliary function is a helpful component to improve language model's code generation ability. However, a systematic exploration of how they affect has yet to be done. In this work, we comprehensively evaluate the ability to utilize…
The constraint of difference is known to the constraint programming community since Lauriere introduced Alice in 1978. Since then, several solving strategies have been designed for this constraint. In this paper we give both a practical…
We consider additive codes over GF(4) that are self-dual with respect to the Hermitian trace inner product. Such codes have a well-known interpretation as quantum codes and correspond to isotropic systems. It has also been shown that these…
Recent advances in Large Language Models (LLMs) have introduced a new paradigm for software development, where source code is generated from natural language prompts. While this paradigm significantly boosts development productivity,…
In this work, we explore explicit Large Language Model (LLM)-powered support for the iterative design of computer programs. Program design, like other design activity, is characterized by navigating a space of alternative problem…
This paper presents a definition of a construction for long polar codes. Recently, we know that partial order is a universal property of the construction with a sublinear complexity for polar codes. In order to describe the partial order,…
Channel coding over arbitrarily-permuted parallel channels was first studied by Willems et al. (2008). This paper introduces capacity-achieving polar coding schemes for arbitrarily-permuted parallel channels where the component channels are…
In this book, the authors introduce the notion of set codes, set bicodes and set n-codes. These are the most generalized notions of semigroup n-codes and group n-codes. Several types of set n-codes are defined. Several examples are given to…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
Brette (2019) criticizes the notion of neural coding because it seems to entail that neural signals need to be decoded by or for some receiver in the head. If that were so, then neural coding would indeed be homuncular (Brette calls it…
Modern languages are equipped with static type checking/inference that helps programmers to keep a clean programming style and to reduce errors. However, the ever-growing size of programs and their continuous evolution require building fast…