generalized gray map
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Generalized Gray map and a class of p-ary nonlinear codes

Finite Fields and Their Applications ◽

10.1016/j.ffa.2015.06.006 ◽

2015 ◽

Vol 36 ◽

pp. 81-97 ◽

Cited By ~ 2

Author(s):

Ziling Heng ◽

Qin Yue

Keyword(s):

Gray Map ◽

Nonlinear Codes ◽

Generalized Gray Map

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Quantum codes over rings

International Journal of Quantum Information ◽

10.1142/s0219749914500208 ◽

2014 ◽

Vol 12 (04) ◽

pp. 1450020 ◽

Cited By ~ 4

Author(s):

Kenza Guenda ◽

T. Aaron Gulliver

Keyword(s):

Linear Codes ◽

Error Correcting Codes ◽

Codes Over Rings ◽

Quantum Codes ◽

Matrix Product ◽

Frobenius Rings ◽

Linear Codes Over Rings ◽

Generalized Gray Map ◽

Css Construction ◽

Quantum Error

This paper considers the construction of quantum error correcting codes from linear codes over finite commutative Frobenius rings. We extend the Calderbank–Shor–Steane (CSS) construction to these rings. Further, quantum codes are extended to matrix product codes. Quantum codes over 𝔽pk are also obtained from linear codes over rings using the generalized Gray map.

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