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This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
This article proposes to auto-encode text at byte-level using convolutional networks with a recursive architecture. The motivation is to explore whether it is possible to have scalable and homogeneous text generation at byte-level in a…
In this paper, we propose a general construction of linear perfect codes over infinite skew fields and quasi skew fields with right (left) unity. A complete classification of such codes over associative skew fields is given. Since the…
Recently, we introduced a new class of finite alphabet iterative decoders (FAIDs) for low-density parity-check (LDPC) codes. These decoders are capable of surpassing belief propagation in the error floor region on the Binary Symmetric…
In this paper, we introduce a novel explicit family of subcodes of Reed-Solomon (RS) codes that efficiently achieve list decoding capacity with a constant output list size. Our approach builds upon the idea of large linear subcodes of RS…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…
Neural network-based image coding has been developing rapidly since its birth. Until 2022, its performance has surpassed that of the best-performing traditional image coding framework -- H.266/VVC. Witnessing such success, the IEEE 1857.11…
In this note, we establish the convexity and monotonicity for affine standard Lyndon words in all types, generalizing the $A$-type results of arXiv:2305.16299. We also derive partial results on the structure of imaginary standard Lyndon…
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…
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…
This paper gives new results for synchronization strings, a powerful combinatorial object that allows to efficiently deal with insertions and deletions in various communication settings: $\bullet$ We give a deterministic, linear time…
The $i$th coordinate of an $(n,k)$ code is said to have locality $r$ and availability $t$ if there exist $t$ disjoint groups, each containing at most $r$ other coordinates that can together recover the value of the $i$th coordinate. This…
This paper proposes a generic formulation that significantly expedites the training and deployment of image classification models, particularly under the scenarios of many image categories and high feature dimensions. As a defining…
We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that…
Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…
Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of…
A unique decoding algorithm for general AG codes, namely multipoint evaluation codes on algebraic curves, is presented. It is a natural generalization of the previous decoding algorithm which was only for one-point AG codes. As such, it…
We use affine variety codes and their subfield-subcodes for obtaining quantum stabilizer codes via the CSS code construction. With this procedure, we get codes with good parameters and a code whose parameters exceed the CSS quantum…
This work introduces self-infilling code generation, a general framework that incorporates infilling operations into auto-regressive decoding. Our approach capitalizes on the observation that recent infilling-capable code language models…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…