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

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