相关论文: Narain CFTs and error-correcting codes on finite f…
We construct a class of chiral fermionic CFTs from classical codes over finite fields whose order is a prime number. We exploit the relationship between classical codes and Euclidean lattices to provide the Neveu-Schwarz sector of fermionic…
Higher genus modular invariance of two-dimensional conformal field theories (CFTs) is a largely unexplored area. In this paper, we derive explicit expressions for the higher genus partition functions of a specific class of CFTs: code CFTs,…
We give two methods for constructing many linear complementary dual (LCD for short) codes from a given LCD code, by modifying some known methods for constructing self-dual codes. Using the methods, we construct binary LCD codes and…
Linear codes with complementary duals are linear codes whose intersection with their duals are trivial, shortly named LCD codes. In this paper we outline a construction for LCD codes over finite fields of order $q$ using weighing matrices…
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…
We provide an algorithm to construct unitary matrices over finite fields. We present various constructions of Hermitian self-dual code by means of unitary matrices, where some of them generalize the quadratic double circulant constructions.…
Recently introduced connections between quantum codes and Narain CFTs provide a simple ansatz to express a modular-invariant function $Z(\tau,\bar \tau)$ in terms of a multivariate polynomial satisfying certain additional properties. These…
In this paper, we determine all self-dual codes over $F_p+vF_p$ ($v^2=v$) in terms of self-dual codes over the finite field $F_p$ and give an explicit construction for self-dual codes over $F_p+vF_p$, where $p$ is a prime.
We describe the general shift orbifold of a Narain CFT and use this to investigate decompactification limits in the heterotic Narain moduli space. We also comment on higher rank theories and describe some applications to the CFT based on…
In this paper quadratic residue codes over the ring Fp + vFp are introduced in terms of their idempotent generators. The structure of these codes is studied and it is observed that these codes share similar properties with quadratic residue…
Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given $n$ and $r<n$, with $n$ or $r$ (or both) odd, MDS LCD $(n,r)$ codes are constructed over finite fields whose…
In this work, we investigate additive complementary dual (ACD) codes and their construction over finite fields $\mathbb{F}_{q^2}$ with respect to the trace inner products, where $q$ is a prime power. First, we associate an additive code…
We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge c > 1 using modular bootstrap. Upper bounds on the gap in the dimension of primary operators of any spin, as well as in the dimension…
We use the embedding formalism to construct conformal fields in $D$ dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in $(D+2)$ dimensions to the projective null cone. Conformal correlators may be…
We derive the spectral domain properties of two-dimensional (2-D) $(\lambda_1, \lambda_2)$-constacyclic codes over $\mathbb{F}_q$ using the 2-D finite field Fourier transform (FFFT). Based on the spectral nulls of 2-D $(\lambda_1,…
In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS…
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…
We extend the TFT construction of CFT correlators of [arXiv:hep-th/0204148] to so-called finite logarithmic CFTs for which the algebraic input data is no longer semisimple but still finite. More specifically, starting from the data of a…
Linear complementary dual (LCD) codes over finite fields are linear codes satisfying $C\cap C^{\perp}=\{0\}$. We generalize the LCD codes over finite fields to $\mathbb{Z}_2\mathbb{Z}_2[u]$-LCD codes over the ring…
We investigate orbifolds of lattice conformal field theories with the goal of constructing theories with large gap. We consider Barnes-Wall lattices, which are a family of lattices with no short vectors, and orbifold by an extraspecial…