Communication has become fundamental in modern society through for instance online banking, mobile communications, and the use of satellites. This means that the need for reliable and secure transmission of digital data is crucial both in our everyday life and in scientific, medicine and military uses. The research on secure and reliable communication we address problems of digital transmission of data focussing on the reliability of the information that is transmitted. One of the main problems in data communication is that the channel through which the data is transmitted may – and normally will- corrupt the data. As an example,  a mobile phone signal sent through the air might be corrupted by environmental noise, or a scratch on a CD will make the data contained on a CD difficult to read. The idea of coding theory is to introduce redundancy in the information in order to be able to detect and correct these errors.

The research concentrates mostly on the efficient decoding of information sent using highly-structured error-correcting codes, using graph-based techniques, applied not only to binary (data is transmitted in bits: 0 and 1), but to larger alphabets. In communications,  it is also important to minimize the bandwidth occupied by transmitted signals, through the design of efficient sequences for information transmission. The address this issue, the group works with the design of sequences that have low interaction, thus facilitating their transmission through the same physical transmission medium. Another problem in communications occur when privacy of the information is important: we want to keep the context of the message (be an e-mail, the number of your credit card, or other sensitive information) secret from possible eavesdroppers. The aim of cryptography is to protect information from eavesdropping. The groups works with finding good Boolean functions (that are often used to encrypt a message) for cryptography, meaning functions that are resilient to certain types of attack.

Quantum computing and quantum communications is a developing area, and the use of graph-based quantum states is very important for this area. The group works on an extension of these states to other type of states which we believe will be useful for quantum computing.