# Carmelo Interlando Ph.D.

## Associate Dean for Academic and Faculty Affairs,

Professor of Mathematics

Phone: 619.594.7237

San Diego State University

College of Sciences GMCS 604 J

5500 Campanile Dr.

San Diego, CA 92182-1010

College of Sciences GMCS 604 J

5500 Campanile Dr.

San Diego, CA 92182-1010

### Education

B.S., State University of Campinas (UNICAMP), Brazil, Computational and Applied Mathematics, 1990

Ph.D., State University of Campinas (UNICAMP), Brazil, Electrical Engineering, 1994

Ph.D., University of Notre Dame, Mathematics, 2005

### Research Interests

Applied Algebra

- Sphere Packings, Lattices, and Number Fields
- Algebraic Coding Theory, Modulation Schemes
- Cryptology and Algorithmic Complexity

### Publications

- Lattices from Abelian extensions and error-correcting codes, to appear in Rocky Mountain Journal of Mathematics, 2021. (T. P. da Nobrega Neto, J. V. L. Nunes, J. O. D. Lopes).
- Fully-diverse lattices from ramified cyclic extensions of prime degree, International Journal of Applied Mathematics, 33(6): 1009-1015, 2020. (A. A. de Andrade, B. Garcia- Malaxechebarria, A. J. Ferrari, R. R. de Araujo).
- Constructions of dense lattices of full diversity, Trends in Applied and Computational Mathematics, 21(2): 299-311, 2020. (A. A. de Andrade, A. J. Ferrari, R. R. de Araujo).
- Generalization of the ball-collision algorithm, Journal of Algebra Combinatorics, Discrete Structures and Applications, 7(2): 195-207, 2020. (K. Khathuria, N. Rohrer, J. Rosenthal, V. Weger).
- Trace forms of certain subfields of cyclotomic fields and applications, Journal of Algebra Combinatorics, Discrete Structures and Applications, 7(2): 141-160, 2020. (A. A. de Andrade, A. J. Ferrari, R. R. de Araujo).
- Constructions of dense lattices over number fields, Trends in Applied and Computational Mathematics, 21(1): 57-63, 2020. (A. A. de Andrade, A. J. Ferrari, R. R. de Araujo).
- A construction of rotated lattices via totally real subfields of the cyclotomic field ℚ(ζ
_{p}), Trends in Applied and Computational Mathematics, 20(3): 561-570, 2019. (A. A. de Andrade, E. Luiz de Oliveira). - Rotated ℤ
^{n}-lattices via real subfields of ℚ(ζ_{2r}), Trends in Applied and Computational Mathematics, 20(3): 445-456, 2019. (A. A. de Andrade). - Construction of even-dimensional lattices of full diversity, International Journal of Applied Mathematics, 32(2): 325-332, 2019. (A. A. de Andrade).
- A new number field construction of the D
_{4}-lattice, International Journal of Applied Mathematics, 31(2): 299-305, 2018. (J. O. D. Lopes, T. P. da Nobrega Neto). - New p-dimensional lattices from cyclic extensions, Journal of Algebra and its Applications, DOI: 10.1142/S0219498817501869, 9 pages, 2017. (J. V. L. Nunes, T. P. da Nobrega Neto, J. O. D. Lopes).
- Four-dimensional lattices from ℚ(2
^{½}, 5^{½}), International Journal of Applied Mathematics, 30(5): 401-408, 2017. (T. P. da Nobrega Neto, J. V. L. Nunes, J. O. D. Lopes). - The integral trace form of cyclic extensions of odd prime degree, Rocky Mountain Journal of Mathematics, 47(4): 1075-1088, 2017. (E. Luiz de Oliveira, Trajano P. da Nóbrega Neto, and J. O. D. Lopes).
- p-Class groups of cyclic number fields of odd prime degree, International Journal of Algebra, 10(9): 429-435, 2016. (J. V. L. Nunes, T. P. da Nobrega Neto, and J. O. D. Lopes).
- Complete hyperbolic lattices derived from tesselations of type {4g, 4g}, Journal of Algebra and its Applications, 15(8), 2016. (C. Q. Queiroz, C. W. Benedito, and R. Palazzo, Jr.).
- An algorithm to construct arithmetic Fuchsian groups derived from quaternion algebras and the corresponding hyperbolic lattices,” Journal of Pure and Applied Algebra, 220(5): 1902-1923, 2016. (C. W. Benedito and R. Palazzo, Jr.).
- Hyperbolic lattices with complete labeling derived from {4g, 4g} tesselations,” R. Pinto, M. Rocha, and P. Vettori, editors, Coding Theory and Applications, 317-325, CIM Series in Mathematical Sciences, Springer, 2015. (C. Q. Queiroz, C. W. Benedito, and R. Palazzo, Jr.).
- A note on the integral trace form in cyclotomic fields, Journal of Algebra and its Applications, 14(4): 2015. (T. P. da Nóbrega Neto, T. M. Rodrigues, and J. O. D. Lopes).
- Two matrix-based lattice construction techniques, Linear Algebra and its Applications, 438(7): 3001-3010, 2013. (T. P. da Nóbrega Neto, A. L. Flores, and J. O. D. Lopes).
- A new number field construction of the lattice E
_{8}, Beiträge zur Algebra und Geometrie/Contributions to Algebra and Geometry, 54(2): 503-508, 2012. (T. P. da Nóbrega Neto, A. L. Flores, and A. L. Contiero). - Algebraic decoding of the ternary (37, 18, 11) quadratic residue code, International Journal of Information and Coding Theory, 2(1): 59-65, 2011.
- Decoding the (41, 20, 10) quadratic residue code beyond its error-correcting capability, Applied Mathematical Sciences, 5(46): 2261-2269, 2011. (Cynthia Padilla).
- An extension of Craig's family of lattices, Canadian Mathematical Bulletin, 54: 645-653, 2011. (A. L. Flores and T. P. da Nóbrega Neto).
- On a refinement of Craig's lattices, Journal of Pure and Applied Algebra, 215: 1440-1442, 2011. (A. L. Flores, T. P. da Nóbrega Neto, and J. O. D. Lopes).
- On the structure of residue rings of prime ideals in algebraic number fields – part II: ramified Primes, International Mathematical Forum, 6(12): 565-589, 2011. (M. Elia and R. Rosenbaum).
- On the minimum absolute value of the discriminant of Abelian fields of degree p
^{2}, Journal of Algebra and its Applications, 9(5): 819-824, 2010. (J. O. D. Lopes, T. P. da Nóbrega Neto, and A. L. Flores). - On the structure of residue rings of prime ideals in algebraic number fields – part I: unramified primes, International Mathematical Forum, 5(56): 2795-2808, 2010. (M. Elia and R. Rosenbaum).
- Optimal families of two and three-dimensional lattice packings from polynomials with integer coefficients, JP Journal of Algebra, Number Theory and Applications, 15(1): 45-51, 2009. (J. V. L. Nunes, T. P. da Nóbrega Neto, and A. L. Flores).
- Decoding the ternary (23, 11, 9) quadratic residue code, Research Letters in Communications, 2009.
- On the computation of the norm-Euclidean minimum of algebraic number fields, International Journal of Algebra, 3(7): 341-354, 2009. (M. Elia).
- Finiteness of the class group of a number field via lattice packings, JP Journal of Algebra, Number Theory and Applications, 13(1): 1-5, 2009. (T. P. da Nóbrega Neto and J. V. L. Nunes).
- A family of asymptotically good lattices having a lattice in each dimension, International Journal of Number Theory, 4(1): 147-154, 2008. (A. L. Flores and T. P. da Nóbrega Neto).
- Quadratic-residue codes and cyclotomic fields, Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications, Springer Netherlands (on line), 2006. (M. Elia).
- The discriminant of Abelian number fields, Journal of Algebra and its Applications, vol. 5, No. 1, pp. 35-41, February 2006. (T. P. da Nóbrega Neto and J. O. D. Lopes).
- On the Effective Computation of Isomorphisms Between σ(O
_{F}/𝔭) and GF(N(𝔭)), Journal of Discrete Mathematical Sciences and Cryptography, vol. 7, No. 2, August 2004. (M. Elia). - Fibonacci ideal lattices in 𝕫[ζ
_{12}], The Fibonacci Quarterly, vol. 41, June-July 2003, N.3, pp.279-288. (M. Elia). - On computing discriminants of subfields of Q(ζ
_{pr}), J. of Number Theory, 96, 319-325 (2002). (T. P. da Nóbrega Neto and J. O. D. Lopes). - Relating propelinear and binary G-linear codes, Discrete Mathematics, vol. 243/1-3, pp. 187-194, December 2001. (M. M. S. Alves, J. R. Gerônimo, R. Palazzo, Jr., and S. R. Costa).
- Lattice constellations and codes from quadratic number fields, IEEE Transactions on Information Theory, vol. 47, pp. 1514-1527, May 2001. (T. P. da Nóbrega Neto, O. M. Favareto, M. Elia, and R. Palazzo, Jr.).
- On the optimality of finite constellations from algebraic lattices, Electronic Notes in Discrete Mathematics, vol. 6, April 2001. (M. Elia and T. P. da Nóbrega Neto).
- Computing the reciprocal of units in finite Galois rings, Journal of Discrete Mathematical Sciences and Cryptography, vol. 3/4, 2000. (M. Elia and R. Palazzo, Jr.).
- New quaternary codes obtained from a combinatorial optimization algorithm, Acta Sci., Univ. Estadual de Maringá, vol. 21, No.4, pp. 881-889, 1999. (J. R. Gerônimo and R. Palazzo Jr.).
- Codes over rings of algebraic integers, Revista da Sociedade Brasileira de Telecomunicações, vol. 13, No. 1, pp. 1-20, June 1998. (O. M. Favareto, T. P. da Nóbrega Neto, and R. Palazzo, Jr.).
- On the decoding of Reed-Solomon and BCH codes over integer residue rings, IEEE Transactions on Information Theory, vol. 43, No. 3, pp. 1213-1221, May 1997. (R. Palazzo, Jr. and M. Elia).
- The symmetry group of 𝕫
_{q}^{n}in the Lee space and the 𝕫_{qn}-linear codes, in Applied Algebra, Algebraic Algorithms and Error Correcting Codes, T. Mora e H. Mattson (Editors), Lecture Notes in Computer Science, No. 1255, Springer Verlag, 1997, pp. 66-77 (J. R. Gerônimo, S. R. Costa, R. Palazzo, Jr. and M. M. S. Alves). - On the decoding of Reed-Solomon codes over integer rings, in Communications, Coding, and Signal Processing, B. Honary, M. Darnell e P. Farrel (Editors), Research Studies Press, Ltd., Taunton, Somerset, England, John Wiley & Sons Inc., 1997, pp. 89-105 (R. Palazzo, Jr. and M. Elia).
- Group block codes over non-abelian groups are asymptotically bad, IEEE Transactions on Information Theory, vol. 42, No. 4, pp. 1277-1280, July 1996. (R. Palazzo, Jr. and M. Elia).
- A note on cyclic codes over 𝕫
_{m}, Latin American Applied Research, vol. 25/S, pp. 83-85, 1995. (R. Palazzo, Jr.). - On the relationship between the diophantine equations over the ring of algebraic integers and the mapping by set partitioning, in Coded Modulation and Bandwidth Efficient Transmission, E. Biglieri and M. Luise (Editors), 1992, Elsevier Science Publishing Co., pp. 79-90. (R. Palazzo, Jr.).

### Editorial Board of Journal

Journal of Discrete Mathematical Sciences and Cryptography

### Affiliation

American Mathematical Society