Aussie AI

Algebraic Integers

Last Updated 12 May, 2026

by David Spuler, Ph.D.

Research on Algebraic Integers

Research papers include:

D. F. G. Coelho, S. Nimmalapalli, V. S. Dimitrov, A. Madanayake, R. J. Cintra and A. Tisserand, 2018, "Computation of 2D 8×8 DCT Based on the Loeffler Factorization Using Algebraic Integer Encoding," in IEEE Transactions on Computers, vol. 67, no. 12, pp. 1692-1702, 1 Dec. 2018, doi: 10.1109/TC.2018.2837755, https://ieeexplore.ieee.org/document/8360454
Wikipedia, May 2026 (accessed), Algebraic integer, https://en.wikipedia.org/wiki/Algebraic_integer
Z. YANG, M. Shang, S. HU, K. ZHENG, X. CAO and J. CHEN, "Design of FIR Filter Based on Algebraic Integer Quantization," 2018 IEEE 23rd International Conference on Digital Signal Processing (DSP), Shanghai, China, 2018, pp. 1-5, doi: 10.1109/ICDSP.2018.8631667, https://ieeexplore.ieee.org/document/8631667
S. Mohammadi and A. Javadi, "An Efficient Technique for Error-Free Implementation of H.264 Using Algebraic Integer Encoding," 2010 International Conference on Signal Acquisition and Processing, Bangalore, India, 2010, pp. 145-150, doi: 10.1109/ICSAP.2010.47, https://ieeexplore.ieee.org/document/5432686
K. A. Wahid, V. S. Dimitrov and G. A. Jullien, "Error-free arithmetic for discrete wavelet transforms using algebraic integers," Proceedings 2003 16th IEEE Symposium on Computer Arithmetic, Santiago de Compostela, Spain, 2003, pp. 238-244, doi: 10.1109/ARITH.2003.1207684. https://ieeexplore.ieee.org/document/1207684
Minyi Fu, V. S. Dimitrov and G. A. Jullien, "An efficient technique for error-free algebraic-integer encoding for high performance implementation of the DCT and IDCT," ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196), Sydney, NSW, Australia, 2001, pp. 906-909 vol. 4, doi: 10.1109/ISCAS.2001.922385. https://ieeexplore.ieee.org/document/922385
Sangho Yun, Fan Wu, G. E. Sobelman and Xiaofang Zhou, "A low-complexity FFT Processor using two-dimensional algebraic integer encoding," 2016 13th IEEE International Conference on Solid-State and Integrated Circuit Technology (ICSICT), Hangzhou, 2016, pp. 737-740, doi: 10.1109/ICSICT.2016.7999028, https://ieeexplore.ieee.org/document/7999028
K. Wahid, V. Dimitrov and G. Jullien, "Error-free computation of 8/spl times/8 2D DCT and IDCT using two-dimensional algebraic integer quantization," 17th IEEE Symposium on Computer Arithmetic (ARITH'05), Cape Cod, MA, USA, 2005, pp. 214-221, doi: 10.1109/ARITH.2005.20, https://ieeexplore.ieee.org/document/1467642
A. Madanayake et al., "A Row-Parallel 8 × 8 2-D DCT Architecture Using Algebraic Integer-Based Exact Computation," in IEEE Transactions on Circuits and Systems for Video Technology, vol. 22, no. 6, pp. 915-929, June 2012, doi: 10.1109/TCSVT.2011.2181232, https://ieeexplore.ieee.org/document/6114256