# A week on coding and information

Days two and three

During days two and three of the LAWCI the talks showed the versatility of coding and information theory, starting from advanced applications to cryptography, until quantum bits. We have learned how to apply finite fields on protocols such as the Advanced Encryption Standard (AES), which is used in whatsapp’s end to end encryption, how to interpret mutations in the DNA, and how to manipulate data with *quantum bits.*

## Student posters

Students presented their ongoing research work during two poster sessions. Besides the sessions, we had a 3-minute elevator pitch presentation for every student. In massive conferences such as ISIT, sometimes we only have three minutes to communicate to our peers during the coffee break, so the presentations served as a good practice for the academic future of the students.

## Quantum errors: the Good, the Bad and the Ugly.

In the afternoons we learned about quantum bits with Prof Markus Grassl (Max Planck Institute, Erlangen, Germany). Prof Grassl is not only a lead academic in Mathematics and Computer Science, but also a renowned harmonica player, including successful international performances of Brazilian music.

Among the weird properties of quantum mechanics, there is the fact that we cannot *copy* bits, known as the *no-cloning theorem*. In spite of this, one can leverage the versatility of quantum mechanics in order to built algorithms that can theoretically perform operations much faster than a classical computer. However, quantum systems are inherently noisier than classical ones, and that’s where IT and Coding Theory come in handy, as explained by Prof Grassl. He also explained that in certain quantum coded systems, there are certain types of “good” noise (error) that leaves the system unaffected, some bad errors can be handled and some ugly errors that will mess everything up.

Quantum computing has already enabled technologies such as quantum experiences (yes, you can operate a quantum computer. yes, you can do that in python!). In spite of that, error correction remains a big challenge and much-needed research direction.

## ACTG is for Coding Theory

In a world where encoding of a digital movie video into the DNA of bacteria is no longer science fiction it seems necessary to ask what is the capacity of data storage of DNA sequence. These and other questions have been discussed by Prof Moshe Schwartz (U ben Gurion) using fine combinatorial techniques. He presented exciting connection between encoding of DNA sequences and combinatorial structures, including formal languages, well-known friends (or foes?) of computer scientists.

## Frames are everywhere

In the border between signal processing and communications, Prof Ram Zamir (Tel Aviv U) talked on how use a fairly general concept of *frames* to add redundancy, remove redudancy and multiplexing data. Prof Zamir had to recover the flash drive with his slides from the Amazon river (thanks for the commitment!).

Prof Zamir explained all main mathematical properties of frames, which have connections to analog codes, wavelets, compressed(-ive) sensing, and the discrete Fourier transform, which led him to the categorical “frames are everywhere” (10 years ago, Prof Zamir stated that lattices are everywhere — maybe both are true?).

**End of the school**

This is the last day of the school. The students have been awarded with world-class researchers, willing to mingle and discuss the most various research topic. The second part of the LAWCI will include the presentation of original research work, along with plenary talks.