Related papers: Transitive and Self-dual Codes Attaining the Tsfas…
Bazzi and Mitter [3] showed that binary dihedral group codes are asymptotically good. In this paper we prove that the dihedral group codes over any finite field with good mathematical properties are asymptotically good. If the…
It is well known that quantum codes can be constructed through classical symplectic self-orthogonal codes. In this paper, we give a kind of Gilbert-Varshamov bound for symplectic self-orthogonal codes first and then obtain the…
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…
In order to perform universal fault-tolerant quantum computation, one needs to implement a logical non-Clifford gate. Consequently, it is important to understand codes that implement such gates transversally. In this paper, we adopt an…
We propose a new systematic construction of CSS-T codes from any given CSS code using a map $\phi$. When $\phi$ is the identity map $I$, we retrieve the construction of [1] and use it to prove the existence of asymptotically good binary…
This paper introduces a framework for constructing Calderbank-Shor-Steane (CSS) codes that support fault-tolerant logical transversal $Z$-rotations. Using this framework, we obtain asymptotically good CSS codes that fault-tolerantly realize…
A finite group with a cyclic normal subgroup N such that G/N is cyclic is said to be metacyclic. A code over a finite field F is a metacyclic code if it is a left ideal in the group algebra FG for G a metacyclic group. Metacyclic codes are…
It was shown by Massey that linear complementary dual (LCD for short) codes are asymptotically good. In 2004, Sendrier proved that LCD codes meet the asymptotic Gilbert-Varshamov (GV for short) bound. Until now, the GV bound still remains…
In 2011, Guruswami-H{\aa}stad-Kopparty \cite{Gru} showed that the list-decodability of random linear codes is as good as that of general random codes. In the present paper, we further strengthen the result by showing that the…
We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum…
A code is called transitive if its automorphism group (the isometry group) of the code acts transitively on its codewords. If there is a subgroup of the automorphism group acting regularly on the code, the code is called propelinear. Using…
The recently introduced tile codes are a promising alternative to surface codes, combining two-dimensional locality with higher encoding efficiency. While surface codes are well understood in terms of their logical operators and boundary…
Two generalizations of the Hartmann--Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique…
In this note, we complete the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups.
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
In this work, our main objective is to construct quantum codes from quasi-twisted (QT) codes. At first, a necessary and sufficient condition for Hermitian self-orthogonality of QT codes is introduced by virtue of the Chinese Remainder…
A class of optimal three-weight cyclic codes of dimension 3 over any finite field was presented by Vega [Finite Fields Appl., 42 (2016) 23-38]. Shortly thereafter, Heng and Yue [IEEE Trans. Inf. Theory, 62(8) (2016) 4501-4513] generalized…
Locally repairable codes have been investigated extensively in recent years due to practical application in distributed storage as well as theoretical interest. However, not much work on asymptotical behavior of locally repairable codes has…
We complete the building-up construction for self-dual codes by resolving the open cases over $GF(q)$ with $q \equiv 3 \pmod 4$, and over $\Z_{p^m}$ and Galois rings $\GR(p^m,r)$ with an odd prime $p$ satisfying $p \equiv 3 \pmod 4$ with…
The Gilbert--Varshamov (GV) bound is a central benchmark in coding theory, establishing existential guarantees for error-correcting codes and serving as a baseline for both Hamming and quantum fault-tolerant information processing. Despite…