Generating Vector Format

A generating vector file stores one generating vector along with information describing the parameters used to construct it. It is stored in the JSON format in a file with extension .json. In the JSON format, everything is represented as a key:value pair- the stored keys are listed in the table below.

Since it would be very inefficient to store the exact sequence $\beta_j$ that is used in the construction for every generating vector, we consider classes of generating vectors constructed by the same parametrization. We then store the parameters of the parametrization instead of the actual values of $\beta_j$.

Generating vectors for various values of $m$ in $N=2^m$ are stored together in either a .tar.gz, .tar.bz2, or .zip archive for download. These links are given on the various pages for different weight types and parametrizations for $\beta_j$.

Key	Value
C	Walsh coefficient bound used in the construction.
P(2)	An integer obtained by evaluating the irreducible polynomial $P\in\mathbb{Z}_2[x]$ at $x=2$.
P(x) ${}_{}$	Vector of coefficients in $\{0,1\}^{m+1}$ of the irreducible polynomial $P$.
WCE	Worst-case error bound computed during CBC construction.
alpha	Interlacing parameter.
entropy	Entropy of the generating vector (1: no entries repeat, 0: all entries repeat).
genvec	The generating vector, represented as a vector of integers (each corresponding to a polynomial as mentioned above).
m	Degree of the irreducible polynomial, number of coefficients of the polynomials of the generating vector, and exponent in the number of points $N=2^m$.
s	Dimension for which this generating vector was constructed (can be used for all dimensions $\le s$).
weight	String specifying the weight type (given under “Weight Type” in the listings).
version	Version of software used to generate the vector. [optional]

For reading and writing JSON files, we recommend jsoncons for C++ and the standard json module for Python. Various libraries exist for other languages.