Related papers: Semidefinite programming bounds for constant weigh…
We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show…
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study the largest minimum weight $d(n,k)$ among all binary linear complementary dual $[n,k]$ codes. We…
We derive refined entropy upper bounds for $q$-ary $B_2$ codes by exploiting the Fourier structure of the i.i.d. difference distribution $D=X-Y$. Since the pmf of $D$ is an autocorrelation, its Fourier series is a nonnegative trigonometric…
We apply the semidefinite programming approach developed in arxiv:math.MG/0608426 to obtain new upper bounds for codes in spherical caps. We compute new upper bounds for the one-sided kissing number in several dimensions where we in…
We are considering RAMs $N_{n}$, with wordlength $n=2^{d}$, whose arithmetic instructions are the arithmetic operations multiplication and addition modulo $2^{n}$, the unary function $ \min\lbrace 2^{x}, 2^{n}-1\rbrace$, the binary…
For a code $C$ in a space with maximal distance $n$, we say that $C$ has symmetric distances if its distance set $S(C)$ is symmetric with respect to $n / 2$. In this paper, we prove that if $C$ is a binary code with length $2n$, constant…
Let $A_q(n,d)$ be the maximum order (maximum number of codewords) of a $q$-ary code of length $n$ and Hamming distance at least $d$. And let $A(n,d,w)$ that of a binary code of constant weight $w$. Building on results from algebraic graph…
Non-overlapping codes are a set of codewords such that the prefix of each codeword is not a suffix of any codeword in the set, including itself. If the lengths of the codewords are variable, it is additionally required that every codeword…
It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…
The completely bounded trace and spectral norms, for finite-dimensional spaces, are known to be efficiently expressible by semidefinite programs (J. Watrous, Theory of Computing 5: 11, 2009). This paper presents two new, and arguably much…
By employing the residue polynomials, a construction of constant-composition codes is given. This construction generalizes the one proposed by Xing[16]. It turns out that when d=3 this construction gives a lower bound of…
This paper gives new methods of constructing {\it symmetric self-dual codes} over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant…
We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular,…
We introduce the concepts of complex Grassmannian codes and designs. Let G(m,n) denote the set of m-dimensional subspaces of C^n: then a code is a finite subset of G(m,n) in which few distances occur, while a design is a finite subset of…
Generalized bicycle (GB) codes is a class of quantum error-correcting codes constructed from a pair of binary circulant matrices. Unlike for other simple quantum code ans\"atze, unrestricted GB codes may have linear distance scaling. In…
Codes defined on graphs and their properties have been subjects of intense recent research. On the practical side, constructions for capacity-approaching codes are graphical. On the theoretical side, codes on graphs provide several…
In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs. We propose two types of bounds for quadratically constrained quadratic programs, quadratic and cubic bounds. For quadratic bounds, we use affine…
A new method of constructing optimum constant weight codes over F_2 based on a generalized $(u, u+v)$ construction is presented. We present a new method of constructing superimposed code $C_{(s_1,s_2,\cdots,s_I)}^{(h_1, h_2, \cdots, h_I)}$…
This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…
In this paper, we construct linear codes over $\mathbb{Z}_4$ with bounded $GC$-content. The codes are obtained using a greedy algorithm over $\mathbb{Z}_4$. Further, upper and lower bounds are derived for the maximum size of DNA codes of…