A doubly constant weight code is a binary code of length n1 + n2, with constant weight w1 + w2, such that the weight of a codeword in the first n1 coordinates is w1. Such codes have applications in obtaining bounds on the sizes of constant weight codes with givenminimum distance. Lower and upper bounds on the sizes of such codes are derived. In particular, we show tight connections between opti...

In this work we present a strong analysis of the testability of a broad, and to date the most interesting known, class of “affine-invariant” codes. Affine-invariant codes are codes whose coordinates are associated with a vector space and are invariant under affine transformations of the coordinate space. Affine-invariant linear codes form a natural abstraction of algebraic properties such as li...

In 2006, Smith et al. published a new table of constant weight codes, updating existing tables originally created by Brouwer et al. This paper improves upon these results by filling in 9 missing constant weight codes, all of which are optimal by the second Johnson bound. This completes the tables for A(n, 16, 9) and A(n, 18, 10) up to n = 63 and corrects some A(n, 14, 8).

A conflict-avoiding code (CAC) C of length n with weight k is a family of binary sequences of length n and weight k satisfying ∑ 0≤t≤n−1 xitxj,t+s ≤ 1 for any distinct codewords xi = (xi0, xi1, . . . , xi,n−1) and xj = (xj0, xj1, . . . , xj,n−1) in C and for any integer s, where the subscripts are taken modulo n. A CAC with maximal code size for given n and k is said to be optimal. A CAC has be...

We present some results on almost maximum distance separable (AMDS) codes and Griesmer codes of dimension 4 over F5. We prove that no AMDS code of length 13 and minimum distance 5 exists, and we give a classification of some AMDS codes. Moreover, we classify the projective strongly optimal Griesmer codes over F5 of dimension 4 for some values of the minimum distance.

The threshold behaviour of negative eigenvalues for Schr\"{o}dinger operators the type \[ H_\lambda=-\frac{d^2}{dx^2}+U+ \lambda\alpha_\lambda V(\alpha_\lambda \cdot) \] is considered. potentials $U$ and $V$ are real-valued bounded functions compact support, $\lambda$ a positive parameter, sequence $\alpha_\lambda$ has finite or infinite limit as $\lambda\to 0$. Under certain conditions on ther...

A code C is Z2Z4-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C by deleting the coordinates outside X (respectively, Y ) is a binary linear code (respectively, a quaternary linear code). In this paper, the rank and dimension of the kernel for Z2Z4-linear codes, which are the corresponding binary codes of Z2Z4-additive codes, are ...