# AT&T Weekly Seminar on Quantum Computing and Quantum Error Correction

** QUANTUM COMPUTATION **
** AND **
** QUANTUM ERROR CORRECTION **

## Title:

Bounds for quantum codes Part I: Additive codes

## Speaker:

- Eric Rains
- AT&T

## Place:

- AT&T Laboratories
- 600 Mountain Avenue
- Murray Hill, NJ
- Murray Hill Building, Room: 2D-101

## Time:

- 2:00 p.m.
- Wednesday, February 5, 1997

Thanks to everyone for registering early AND arriving early.
**ABSTRACT:**

One of the fundamental problems in the theory of quantum error
correcting codes is that of finding good upper bounds on the minimum
distance of a code of specified length and dimension. In part I, I will
discuss this problem in the special case when the code is additive (i.e.,
is derived from a code over GF(4)). In this case, the problem is purely
combinatorial, thus allowing standard coding-theory techniques to be
adapted. In particular, the linear programming bound of classical coding
theory can be adapted to give bounds for additive codes. I will also
discuss the concept of the shadow of an additive code, the source of much
of the power of the LP bound in the quantum setting.

This talk is based on joint work with A.R. Calderbank, P.W. Shor,
and N.J.A. Sloane.

**contact:**

- Andre Berthiaume
- email: berthiau@research.att.com
- tel: (908) 582-7911
- URL: http://www.research.att.com/~berthiau

Document last modified on January 31, 1997