222
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127. Pereira, F.R.F., La Guardia, G.G., de Assis, F.M.: Classical and quantum convolutional codes
derived from algebraic geometry codes. IEEE Trans. Commun. 67, 73–82 (2019)
128. Pérez, J.A.D., Porras, J.M., Sotelo, G.S.: Convolutional codes of Goppa type. A.A.E.C.C. 91,
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129. Peterson, W.W., Weldon Jr., E.J.: Error-Correcting Codes. MIT Press, Cambridge (1972)
130. Piret, Ph.: Convolutional Codes: An Algebraic Approach. The MIT Press, Cambridge (1988)
131. Piret, Ph.: A convolutional equivalent to Reed-Solomon codes. Philips J. Res. 43, 441–458
(1988)
132. Rains, E.M.: Quantum codes of minimum distance two. IEEE Trans. Inf. Theory 45, 266–271
(1999)
133. Rains, E.M.: Nonbinary quantum codes. IEEE Trans. Inf. Theory 45, 1827–1832 (1999)
134. Rains, E.M.: Quantum shadow enumerators. IEEE Trans. Inf. Theory 45, 2361–2366 (1999)
135. Rosenthal, J., Smarandache, R.: Maximum distance separable convolutional codes. Appl.
Algebra Eng. Commun. Comput. 10, 15–32 (1998)
136. Rosenthal, J., York, E.V.: BCH convolutional codes. IEEE Trans. Inf. Theory 45, 1833–1844
(1999)
137. Rotman, J.J.: Advanced Modern Algebra. Prentice Hall (2003)
138. Sarvepalli, P.K., Klappenecker, A.: Nonbinary quantum Reed-Muller codes. In: International
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139. Sarvepalli, P.K., Klappenecker, A., Rötteler, M.: Asymmetric quantum LDPC codes. In: International Symposium on Information Theory (ISIT), Toronto, Canada, 6–11 July 2008
140. Sarvepalli, P.K., Klappenecker, A., Rötteler, M.: Asymmetric quantum codes: constructions,
bounds and performance. Proc. R. Soc. A 465, 1645–1672 (2009)
141. Sharma, A., Bakshi, G.K., Dumir, V.C., Raka, M.: Cyclotomic number and primitive idempotents in the ring G F(q)/(x p n − 1). Finite Fields Appl. 10, 653–673 (2004)
142. Sharma, A., Bakshi, G.K., Raka, M.: The weight distributions of irreducible cyclic codes of
length 2 m . Finite Fields Appl. 13, 1086–1095 (2007)
143. Sharma, A., Bakshi, G.K., Raka, M.: Polyadic codes of prime power length. Finite Fields
Appl. 13, 1071–1085 (2007)
144. Shor, P.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 54,
R2493–R2496 (1995)
145. Smarandache, R., Gluesing-Luerssen, H., Rosenthal, J.: Constructions of MDS-convolutional
codes. IEEE Trans. Inf. Theory 47, 2045–2049 (2001)
146. Soares Jr., W.S., Silva, E.B.: Hyperbolic quantum color codes. Quantum Inf. Comput. 18,
0307–0381 (2018)
147. Steane, A.M.: Simple quantum error correcting-codes. Phys. Rev. A 54, 4741–4751 (1996)
148. Steane, A.: Enlargement of Calderbank-Shor-Steane quantum codes. IEEE Trans. Inf. Theory
45, 2492–2495 (1999)
149. Stephens, A.M., Evans, Z.W.E., Devitt, S.J., Hollenberg, L.C.L.: Asymmetric quantum error
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150. Stichtenoth, H.: Self-dual Goppa codes. J. Pure Appl. Algebra 55, 199–211 (1988)
151. Stichtenoth, H.: Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound.
IEEE Trans. Inf. Theory 52, 2218–2224 (2006)
152. Stichtenoth, H.: Algebraic Function Fields and Codes. Springer, Berlim (2009)
153. Sundeep, B., Thangaraj, A.: Self-orthogonality of q-ary images of q m -ary codes and quantum
code construction. IEEE Trans. Inf. Theory 53, 2480–2489 (2007)
154. Tan, P., Li, J.: Efficient quantum stabilizer codes: LDPC and LDPC-convolutional constructions. IEEE Trans. Inf. Theory 56, 476–491 (2010)
155. Thangaraj, A., McLaughlin, S.: Quantum codes from cyclic codes over G F(4 m ). IEEE Trans.
Inf. Theory 47, 1176–1178 (2001)
156. Tonchev, V.D.: Quantum codes from caps. Discret. Math. 308, 6368–6372 (2008)
References
126. Pellikaan, R., Shen, B.-Z., van Wee, G.J.M.: Which linear codes are algebraic-geometric?
IEEE Trans. Inf. Theory 37, 583–602 (1991)
127. Pereira, F.R.F., La Guardia, G.G., de Assis, F.M.: Classical and quantum convolutional codes
derived from algebraic geometry codes. IEEE Trans. Commun. 67, 73–82 (2019)
128. Pérez, J.A.D., Porras, J.M., Sotelo, G.S.: Convolutional codes of Goppa type. A.A.E.C.C. 91,
51–61 (2004)
129. Peterson, W.W., Weldon Jr., E.J.: Error-Correcting Codes. MIT Press, Cambridge (1972)
130. Piret, Ph.: Convolutional Codes: An Algebraic Approach. The MIT Press, Cambridge (1988)
131. Piret, Ph.: A convolutional equivalent to Reed-Solomon codes. Philips J. Res. 43, 441–458
(1988)
132. Rains, E.M.: Quantum codes of minimum distance two. IEEE Trans. Inf. Theory 45, 266–271
(1999)
133. Rains, E.M.: Nonbinary quantum codes. IEEE Trans. Inf. Theory 45, 1827–1832 (1999)
134. Rains, E.M.: Quantum shadow enumerators. IEEE Trans. Inf. Theory 45, 2361–2366 (1999)
135. Rosenthal, J., Smarandache, R.: Maximum distance separable convolutional codes. Appl.
Algebra Eng. Commun. Comput. 10, 15–32 (1998)
136. Rosenthal, J., York, E.V.: BCH convolutional codes. IEEE Trans. Inf. Theory 45, 1833–1844
(1999)
137. Rotman, J.J.: Advanced Modern Algebra. Prentice Hall (2003)
138. Sarvepalli, P.K., Klappenecker, A.: Nonbinary quantum Reed-Muller codes. In: International
Symposium on Information Theory (ISIT), Adelaide, Australia, 4–9 Sept 2005
139. Sarvepalli, P.K., Klappenecker, A., Rötteler, M.: Asymmetric quantum LDPC codes. In: International Symposium on Information Theory (ISIT), Toronto, Canada, 6–11 July 2008
140. Sarvepalli, P.K., Klappenecker, A., Rötteler, M.: Asymmetric quantum codes: constructions,
bounds and performance. Proc. R. Soc. A 465, 1645–1672 (2009)
141. Sharma, A., Bakshi, G.K., Dumir, V.C., Raka, M.: Cyclotomic number and primitive idempotents in the ring G F(q)/(x p n − 1). Finite Fields Appl. 10, 653–673 (2004)
142. Sharma, A., Bakshi, G.K., Raka, M.: The weight distributions of irreducible cyclic codes of
length 2 m . Finite Fields Appl. 13, 1086–1095 (2007)
143. Sharma, A., Bakshi, G.K., Raka, M.: Polyadic codes of prime power length. Finite Fields
Appl. 13, 1071–1085 (2007)
144. Shor, P.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 54,
R2493–R2496 (1995)
145. Smarandache, R., Gluesing-Luerssen, H., Rosenthal, J.: Constructions of MDS-convolutional
codes. IEEE Trans. Inf. Theory 47, 2045–2049 (2001)
146. Soares Jr., W.S., Silva, E.B.: Hyperbolic quantum color codes. Quantum Inf. Comput. 18,
0307–0381 (2018)
147. Steane, A.M.: Simple quantum error correcting-codes. Phys. Rev. A 54, 4741–4751 (1996)
148. Steane, A.: Enlargement of Calderbank-Shor-Steane quantum codes. IEEE Trans. Inf. Theory
45, 2492–2495 (1999)
149. Stephens, A.M., Evans, Z.W.E., Devitt, S.J., Hollenberg, L.C.L.: Asymmetric quantum error
correction via code conversion. Phys. Rev. A 77, 062335(1–5) (2008)
150. Stichtenoth, H.: Self-dual Goppa codes. J. Pure Appl. Algebra 55, 199–211 (1988)
151. Stichtenoth, H.: Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound.
IEEE Trans. Inf. Theory 52, 2218–2224 (2006)
152. Stichtenoth, H.: Algebraic Function Fields and Codes. Springer, Berlim (2009)
153. Sundeep, B., Thangaraj, A.: Self-orthogonality of q-ary images of q m -ary codes and quantum
code construction. IEEE Trans. Inf. Theory 53, 2480–2489 (2007)
154. Tan, P., Li, J.: Efficient quantum stabilizer codes: LDPC and LDPC-convolutional constructions. IEEE Trans. Inf. Theory 56, 476–491 (2010)
155. Thangaraj, A., McLaughlin, S.: Quantum codes from cyclic codes over G F(4 m ). IEEE Trans.
Inf. Theory 47, 1176–1178 (2001)
156. Tonchev, V.D.: Quantum codes from caps. Discret. Math. 308, 6368–6372 (2008)