CODING THEORY AND CRYPTOGRAPHY 

final ctc logo 1 aug 31 2012


The initiatives on coding theory and cryptography came to be in 2005 when Dr. Virgilio P. Sison completed his doctoral dissertation which dealt specifically with the construction of convolutional codes over the integer ring Z_{p^r} from linear block codes over the Galois ring GR(p^r,m). The distance of the block code provides a lower bound for the free distance of the convolutional code. The dissertation, which was supervised by Dr. Patrick Solé of CNRS, France, was published in the journal IEEE Transactions on Information Theory [3] and is now being cited as one of the construction methods for ring convolutional codes.

Dr. Sison has concentrated his research on the derivation of bounds for the distances of convolutional codes and codes over rings. On the side, new structural properties of finite rings, specifically Galois rings and finite Frobenius rings, are determined. Two other papers were published. The first, which generalizes Rabizzoni’s bound (1989), appeared in the IEEE Transactions on Information Theory [4], and is now being cited by MAGMA [5] as a reference for codes over Galois rings. The second, which generalizes Heller’s bound (1968), was presented in the International Conference in Mathematics and its Applications in Bangkok, Thailand in 2007, and was published in Matimyás Matematika, the official journal of the Mathematical Society of the Philippines [6]. Several other papers that resulted from Dr. Sison’s supervision of undergraduate and graduate researches were presented in local or international conferences and workshops. These papers are listed in the Research Outputs Section. Students and faculty members who were advised by Dr. Sison in their undergraduate and graduate researches are the members of the cluster.
At present, the cluster concentrates on the algebraic properties of block codes and convolutional codes over rings, the construction of convolutional codes from block codes, the derivation of certain distance bounds, and the structural properties of finite rings, particularly $F_{p^k} + u F_{p^k}$.

Objectives

The objectives of the cluster are the following:

  1. to help revitalize research in the Division by sustaining its cluster activities through long-term research projects with system funding, presentation of papers in conferences, publication in refereed journals, and sponsorship of seminars, conferences and schools on coding theory;
  2. to assist the Institute in its faculty development program by helping its members to obtain opportunities for trainings and workshops in coding theory and to complete their graduate research requirements;
  3. to support the curricular initiatives of the Division by proposing new courses on coding theory and cryptography; and finally,
  4. to foster collaboration among the different units of the University through inter-disciplinary researches.

Research Themes 

  • Algebraic properties, construction and distance related aspects of block codes (e.g. cyclic, quasi-cyclic, abelian, quasi-abelian and duadic codes);
  • Convolutional codes, subspace codes, Grassmannian codes, and rank-metric codes;
  • Structural properties of special types of finite commutative rings and matrix rings;
  • Application of coding theory in molecular biology

Members

  • Dr. Virgilio P. Sison (Cluster Coordinator) 
  • Prof. Herbert S. Palines
  • Prof. John Mark T. Lampos
  • Prof.Jane D. Palacio
  • Mr. Ben Paul C. Dela Cruz

The cluster counts as associate members the undergraduate students who are doing special problem researches in coding theory. It may invite affiliate members from other units in the University.

Future Plans

The cluster hopes to involve more students and faculty members in coding theory and cryptography. This may be addressed by the new graduate course (MATH 215 – Coding Theory and Cryptography) and MATH 200 (Undergraduate Thesis in Mathematics), the institution of which was initiated by the cluster. The course MATH 215 had six (6) students in its initial offering (first semester 2012-2013). The cluster also intends to explore more fields where coding theory and cryptography may be applied, such as digitization and DNA coding theory.

Publications 

[1] P. Solé and V. Sison, “Bounds on the minimum homogeneous distance of the pr-ary image of linear block codes over the Galois ring GR(pr,m),” IEEE Transactions in Information Theory, vol. 53, no. 6, pp. 2270-2273, June 2007; also in the refereed Proceedings of the 2007 IEEE International Symposium on Information Theory (ISIT 2007), Acropolis Congress and Exhibition Center, Nice, France, pp. 1971-1974, 24-29 June 2007.

[2] P. Solé and V. Sison, “Quaternary convolutional codes from linear block codes over Galois rings,” IEEE Transactions in Information Theory (ISIT 2007), vol. 53, no. 6, pp. 2267-2270, June 2007; also in the refereed Proceedings of the 2007 IEEE International Symposium on Information Theory, (ISIT 2007), Acropolis Congress and Exhibition Center, Nice, France, pp. 2641-2645, 24-29 June 2007.

[3] J.M. Lampos and V. Sison, ``Bounds on the $p^k$-ary image of linear block codes over the semi-local Frobenius ring $\FF_{p^k}+v\FF_{p^k}$," accepted for publication in Southeast Asian J. of Sciences, 2012.

[4] H. Palines and V. Sison, ``On self-dual convolutional codes over rings," accepted for publication in Southeast Asian J. of Sciences, 2012.

[5] V. Sison, “Homogeneous bounds for the image of linear block codes over Galois ring extensions,” Matimyàs Matematika, Journal of the Mathematical Society of the Philippines, vol. 30, nos. 2-3, pp. 113-116, 2007.

[6]  V. Sison, “Heller-type bounds for the homogeneous free distance of convolutional codes over finite Frobenius rings,” Matimyàs Matematika, Journal of the Mathematical Society of the Philippines, vol. 30, no. 1, pp. 23-30, 2007; also in the Collection of Presented Papers of the International Conference in Mathematics and Applications (ICMA-MU 2007), The Century Park Hotel, Bangkok, Thailand, pp. 483-489, August 2007.

[7] B.R. Cerezo, A.M. Pasion and V. Sison, “Binary convolutional codes and linear block codes over $\FF_4$,” Matimyàs Matematika, Journal of the Mathematical Society of the Philippines, vol. 29, no. 1-2, pp. 9-17, 2006; also in the peer-reviewed Pre-proceedings of the 3rd Symposium on the Mathematical Aspects of Computer Science} (SMACS 2006), pp. 77-86, October 2006.

Last Updated on Thursday, 28 September 2017 08:44

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