**Random Research Highlight**: **Hyperdense coding.**
The modulo 6 representation of polynomial *f* is just any
polynomial *f+6g*, that is, we do not care about terms
multiplied by 6. The 6-strong representation of *f* modulo 6
is polynomial *f+2g+3h*, where no two of *g, f* and *h*
have common monomials. Some surprising applications are given: it is
shown that *n* homogeneous linear polynomials can be linearly
transformed to *o(n)* linear polynomials, such that from these
linear polynomials one can get back the 6-strong representations of
the original ones with linear transformations. Probabilistic Memory
Cells (PMC's) are defined, and it is shown that one can encode n
bits into *n* PMC's, transform *n* PMC's to *o(n)*
PMC's ( we call this Hyperdense Coding), and one can transform back
these *o(n)* PMC's to* n *PMC's, and from these one can
get back the original bits. A method is given for converting *n
x n* matrices to *o(n) x o(n)* matrices and from
these tiny matrices one can retrieve 6-strong representations of the
original ones with linear transformations. Note: This is not an LZW-like data compression method: We can compress and reconstruct Kolmogorov-random sequences as well.

IEEE Transactions on Information Theory.Volume
54, Issue 8, pp. 3687-3692, Aug. 2008