Construction of self dual codes from graphs

Fellah, Nazahet
Guenda, Kenza
Özbudak, Ferruh
Seneviratne, Padmapani
In this work we define and study binary codes C-q,C-k and (C-q,C-k) over bar obtained from neighbor- hood designs of Paley-type bipartite graphs P(q, k) and their complements, respectively for q an odd prime. We prove that for some values of q and k the codes C-q,C-k are self-dual and the codes (C-q,C-k) over bar are self-orthogonal. Most of these codes tend to be with optimal or near optimal parameters. Next, we extend the codes C(q,k )to get doubly even self dual codes and find that most of these codes are extremal.


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Peker, Ahmet Gökhan; Yücel, Melek Diker; Department of Electrical and Electronics Engineering (2018)
Polar codes, introduced by Arıkan, are linear block codes that can achieve the capacity of symmetric binary-input discrete memoryless channels with low encoding and decoding complexity. Polar codes of block length N are constructed by channel polarization method, which consists of channel combining and splitting operations to obtain N polarized subchannels from N copies of binary-input discrete memoryless channels. As N grows, symmetric channel capacities of the polarized subchannels converge to either 0 or...
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Probabilistic simultaneous polynomial reconstruction algorithm of Bleichenbacher-Kiayias-Yung is extended to the polynomials whose degrees are allowed to be distinct. Furthermore, it is observed that probability of the algorithm can be increased. Specifically, for a finite field $\F$, we present a probabilistic algorithm which can recover polynomials $p_1,\ldots, p_r \in \F[x]$ of degree less than $k_1,k_2,\ldots,k_r$, respectively with given field evaluations $p_l(z_i) = y_{i,l}$ for all $i \in I$, $
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We show that any joint probability mass function (PMF) can be expressed as a product of parity check factors an d factors of degree one with the help of some auxiliary variables, if the alphabet size is appropriate for defining a parity chec k equation. In other words, marginalization of a joint PMF is equivalent to a soft decoding task as long as a finite field can be constructed over the alphabet of the PMF. In factor graph terminology this claim means that a factor graph representing such a joint PMF alw...
Citation Formats
N. Fellah, K. Guenda, F. Özbudak, and P. Seneviratne, “Construction of self dual codes from graphs,” APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: