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We present a decoder for nonbinary CWS quantum codes using the structure of union codes. The decoder runs in two steps: first, we use a union of stabilizer codes to detect a sequence of errors, and second, we build a new code, called union code, that allows the error correction.
The central objective of this dissertation was to present the Goppa Geometry Codes via elementary methods which were introduced by J.H. van Lint, R.Pellikaan and T. Høhold about 1998. On the first part of such dissertation are presented the fundamental concepts about fields of rational functions of an algebraic curve in the direction as to define the Goppa… (More)
It is known that nonadditive quantum codes are more optimal for error correction when compared to stabilizer codes. The class of codeword stabilized codes (CWS) provides tools to obtain new nonadditive quantum codes by reducing the problem to finding nonlinear classical codes. In this work, we establish some results on the kind of non-Pauli operators that… (More)