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An encoder/decoder map for an $n$-bit binary block code of constant
Hamming weight $w$ is viewed as a bijection between sets $\Lambda_P \bigcap P$ and $\Lambda_Q \bigcap Q$, where $\Lambda_P, \Lambda_Q \subset \mathbb{R}^w$ are integer lattices and $P, Q\subset \mathbb{R}^w$ are bounding polytopes. $P$ and $Q$ are referred to as information and code polytopes, respectively. The desired
bijection is constructed by first dissecting $P$ and $Q$ so that $P=\bigcup_{i=1}^nP_i$ and $Q=\bigcup_{i=1}^nQ_i$ ($n$ is finite), and  then constructing 
invertible linear transformations between corresponding pieces $\Gamma_i: P_i \rightarrow Q_i$, $i=1,2,\ldots,n$. In the
first part of this talk, we describe the dissections of $P$ and $Q$ and
the transformations $\Gamma_i$, $i=1,2,\ldots,n$.  In the second part of the talk,
we describe how these transformations can be modified to ensure that lattice
points are mapped to lattice points, i.e., we describe how to  obtain
mappings $\tilde{\Gamma}_i: \Lambda_P \bigcap P_i \rightarrow \Lambda_Q \bigcap Q_i$, $i=1,2,\ldots,n$. In the process we establish a surprising connection with integer-integer
transformations used in the transform coding literature.
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