Related papers: Embedding in $q$-ary $1$-perfect codes and partiti…
The doubly shortened perfect codes of length 13 are classified utilizing the classification of perfect codes in [P.R.J. \"Osterg{\aa}rd and O. Pottonen, The perfect binary one-error-correcting codes of length 15: Part I - Classification,…
Code concatenation combines two or more component codes to design larger codes with greater noise resilience. Introducing entanglement assistance to concatenated codes provides a further advantage in terms of improved error rates and…
In this paper, the problem of correction of a single error in $q$-ary symmetric channel with noiseless feedback is considered. We propose an algorithm to construct codes with feedback inductively. For all prime power $q$ we prove that two…
In this paper, we use linear codes to study zero-error Slepian-Wolf coding of a set of sources with deviation symmetry, where the sources are generalization of the Hamming sources over an arbitrary field. We extend our previous codes,…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
Perfect error correcting codes allow for an optimal transmission of information while guaranteeing error correction. For this reason, proving their existence has been a classical problem in both pure mathematics and information theory.…
The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to…
For a linear Hamming metric code of length n over a finite field, the number of distinct weights of its codewords is at most n. The codes achieving the equality in the above bound were called full weight spectrum codes. In this paper we…
A code over GF$(q^m)$ can be imaged or expanded into a code over GF$(q)$ using a basis for the extension field over the base field. The properties of such an image depend on the original code and the basis chosen for imaging. Problems…
Subspace codes are the $q$-analog of binary block codes in the Hamming metric. Here the codewords are vector spaces over a finite field. They have e.g. applications in random linear network coding, distributed storage, and cryptography. In…
The projective space of order $n$ over the finite field $\Fq$, denoted here as $\Ps$, is the set of all subspaces of the vector space $\Fqn$. The projective space can be endowed with distance function $d_S(X,Y) = \dim(X) + \dim(Y) -…
We investigate the structure of intersecting error-correcting codes, with a particular focus on their connection to matroid theory. We establish properties and bounds for intersecting codes with the Hamming metric and illustrate how these…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
A large body of the literature of automated program repair develops approaches where patches are generated to be validated against an oracle (e.g., a test suite). Because such an oracle can be imperfect, the generated patches, although…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
Recently, code language models have achieved notable advancements in addressing a diverse array of essential code comprehension and generation tasks. Yet, the field lacks a comprehensive deep dive and understanding of the code embeddings of…
Text embeddings are essential for many tasks, such as document retrieval, clustering, and semantic similarity assessment. In this paper, we study how to contrastively train text embedding models in a compute-optimal fashion, given a suite…
We provide a systematic way of constructing entanglement-assisted quantum error-correcting codes via graph states in the scenario of preexisting perfectly protected qubits. It turns out that the preexisting entanglement can help beat the…
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…