Publications (23)
On linear codes with one-dimensional Euclidean hull and their applications to EAQECCs
Lin Sok
The Euclidean hull of a linear code is the intersection of with its Euclidean dual . The hull with low dimensions gets much interest due to its crucial role in det…
Lower bounds on the minimum distance of long codes in the Lee metric
Hugues Randriam, Lin Sok, Patrick Solé
The Gilbert type bound for codes in the title is reviewed, both for small and large alphabets. Constructive lower bounds better than these existential bounds are derived from geome…
Classification of extremal and -extremal binary self-dual codes of length 38
Carlos Aguilar-Melchor, Philippe Gaborit, Jon-Lark Kim +2
In this paper we classify all extremal and -extremal binary self-dual codes of length 38. There are exactly 2744 extremal self-dual codes, two -extremal $[38,19,6…
The punctured dodecacode is unique
Markus Grassl, Denis Krotov, Lin Sok +1
The punctured dodecacode is an additive -ary code of length and distance which is uniformly packed. We show that a code with the same weight distribution is equivalent…
Hermitian Hulls of Rational Algebraic Geometry Codes and Applications in Quantum Codes
Lin Sok, Martianus Frederic Ezerman, Ling San
Interest in the hulls of linear codes has been growing rapidly. More is known when the inner product is Euclidean than Hermitian. A shift to the latter is gaining traction. The foc…
On self-dual and LCD double circulant and double negacirculant codes over
Minjia Shi, Hongwei Zhu, Liqin Qian +2
Double circulant codes of length over the semilocal ring are studied when is an odd prime power, and is a square in $\mat…
On constacyclic codes over and their Gray images
Minjia Shi, Liqing Qian, Lin Sok +2
We first define a new Gray map from to , where and study -constacyclic codes over . Also of interest are some…
Decomposition of bent generalized Boolean functions
Lin Sok, MinJia Shi, Patrick Solé
A one to one correspondence between regular generalized bent functions from $\F_2^n$ to and tuples of Boolean bent functions is established. This correspondence map…
New Classes of -ary Few Weights Codes
Minjia Shi, Rongsheng Wu, Liqin Qian +2
In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p}…
New families of self-dual codes
Lin Sok
In the recent paper entitled "Explicit constructions of MDS self-dual codes" accepted in { IEEE Transactions on Information Theory}, doi: 10.1109/TIT.2019.2954877, the author has c…
Double circulant self-dual and LCD codes over Galois rings
Minjia Shi, Daitao Huang, Lin Sok +1
This paper investigates the existence, enumeration and asymptotic performance of self-dual and LCD double circulant codes over Galois rings of characteristic and order …
Trace codes over and Boolean function
Minjia Shi, Yan Liu, Randriam Hugues +2
We construct trace codes over by using Boolean functions and skew sets, respectively. Their Lee weight distribution is studied by using a Galois ring version of the Walsh-Ha…
The combinatorics of LCD codes: Linear Programming bound and orthogonal matrices
Steven T. Dougherty, Jon-Lark Kim, Buket Ozkaya +2
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 desig…
MDS linear codes with one dimensional hull
Lin Sok
We define the Euclidean hull of a linear code as the intersection of and its Euclidean dual . The hull with low dimensions gets much interest due to its crucial ro…
Hulls of special typed linear codes and constructions of new EAQECCs
Lin Sok
In this paper, we study Euclidean and Hermitian hulls of generalized Reed-Solomon codes and twisted generalized Reed-Solomon codes, as well as the Hermitian hulls of Roth-Lempel ty…
Construction of optimal Hermitian self-dual codes from unitary matrices
Lin Sok
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 t…
New Classes of -ary Few Weights Codes
Minjia Shi, Rongsheng Wu, Liqin Qian +2
In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p}…
Lattice Codes for the Binary Deletion Channel
Lin Sok, Patrick Solé, Aslan Tchamkerten
The construction of deletion codes for the Levenshtein metric is reduced to the construction of codes over the integers for the Manhattan metric by run length coding. The latter co…
On Linear Codes Whose Hermitian Hulls are MD
Gaojun Luo, Lin Sok, Martianus Frederic Ezerman +1
Hermitian hulls of linear codes are interesting for theoretical and practical reasons alike. In terms of recent application, linear codes whose hulls meet certain conditions have b…
Explicit constructions of optimal linear codes with Hermitian hulls and their application to quantum codes
Lin Sok
We prove that any Hermitian self-orthogonal code gives rise to an code with dimensional Hermitian hull for . We present a ne…
Construction of MDS self-dual codes from orthogonal matrices
Minjia Shi, Lin Sok, Patrick Solé
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 exten…
Constructions of optimal LCD codes over large finite fields
Lin Sok, Minjia Shi, Patrick Solé
In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields…
New families of quantum stabilizer codes from Hermitian self-orthogonal algebraic geometry codes
Lin Sok
There has been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes, using Hermitian self-orthogonal codes, see…