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Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs.…
In this paper, we consider the problem of variable packet-error coding, which emerges in network communication scenarios where a source transmits information to a destination through multiple disjoint paths. The objective is to design codes…
We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query…
Large Language Models (LLMs) have made tremendous strides in code generation, but existing research fails to account for the dynamic nature of software development, marked by frequent library updates. This gap significantly limits LLMs'…
Vibe Coding (VC) is a form of software development assisted by generative AI, in which developers describe the intended functionality or logic via natural language prompts, and the AI system generates the corresponding source code. VC can…
Previous work by the authors on parity-preserving fixed-length constrained encoders is extended to the variable-length case. Parity-preserving variable-length encoders are formally defined, and, to this end, Kraft conditions are developed…
The variable-length Reverse Multi-Delimiter (RMD) codes are known to represent sequences of unbounded and unordered integers. When applied to data compression, they combine a good compression ratio with fast decoding. In this paper, we…
Recently, there has been a surging interest in using large language models (LLMs) for Verilog code generation. However, the existing approaches are limited in terms of the quality of the generated Verilog code. To address such limitations,…
The rapid advancement of large language models (LLMs) has revolutionized code generation tasks across various programming languages. However, the unique characteristics of programming languages, particularly those like Verilog with specific…
Fibonacci codes are self-synchronizing variable-length codes that are proven useful for their robustness and compression capability. Asymptotically, these codes provide better compression efficiency as the order of the underlying Fibonacci…
Two classes of turbo codes over high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (dv=2,dc=3) low-density parity-check code ensemble. A first construction is derived as a…
The advent of large language models trained on code (code LLMs) has led to significant progress in language-to-code generation. State-of-the-art approaches in this area combine LLM decoding with sample pruning and reranking using test cases…
The penalty incurred by imposing a finite delay constraint in lossless source coding of a memoryless source is investigated. It is well known that for the so-called block-to-variable and variable-to-variable codes, the redundancy decays at…
The concept of group divisible codes, a generalization of group divisible designs with constant block size, is introduced in this paper. This new class of codes is shown to be useful in recursive constructions for constant-weight and…
Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area…
The unit-derived method in coding theory is shown to be a unique optimal scheme for constructing and analysing codes. In many cases efficient and practical decoding methods are produced. Codes with efficient decoding algorithms at maximal…
We collect several observations that concern variable-length coding of two-sided infinite sequences in a probabilistic setting. Attention is paid to images and preimages of asymptotically mean stationary measures defined on subsets of these…
In this work we consider a generalization of the well-studied problem of coding for ``stuck-at'' errors, which we refer to as ``strong stuck-at'' codes. In the traditional framework of stuck-at codes, the task involves encoding a message…
In this paper, we consider the problem of variable-length source coding allowing errors. The exponential moment of the codeword length is analyzed in the non-asymptotic regime and in the asymptotic regime. Our results show that the smooth…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…