Quantum punctured Reed-Muller codes

Wei‐Yao Wang

Ilya I. Dumer, Kirill Shabunov

Pradeep Kiran Sarvepalli, Andreas Klappenecker

We construct nonbinary quantum codes from classical generalized Reed-Muller codes and derive the conditions under which these quantum codes can be punctured. We provide a partial answer to a question raised by Grassl, Beth and Rotteler on the existence of q-ary quantum MDS codes of length n with q les n les q2- 1

Pavan Kumar, Noor Mohammad Khan

Do Jun Rhee

It is well known that Reed-Muller (RM) codes are not linear unequal error protection (LUEP) codes because the set of minimum-weight vectors span Reed-Muller codes (punctured or not). In this paper, we show that most RM codes are LUEP codes if RM codes are encoded with a recursively decomposed trellis oriented generator matrix (TOGM) and maximum-likelihood trellis decoding is used.

Giuliano G. La Guardia