Hong-Yeop Song

A Note on Low-Correlation Zone Signal Sets

In this correspondence, we present a connection between designing low-correlation zone (LCZ) sequences and the results of correlation of sequences with subfield decompositions presented in a recent book by the first two authors. This results in LCZ signal sets with huge sizes over three different alphabetic sets: finite field of size, integer residue ring modulo , and the subset in the complex field which consists of powers of a primitive th root of unity. We show a connection between these sequence designs and ldquocompletely noncyclicrdquo Hadamard matrices and a construction for those sequences. We also provide some open problems along this direction.

One-error linear complexity over F p of Sidelnikov sequences

Let p be an odd prime and m be a positive integer. In this paper, we prove that the one-error linear complexity over Fp of Sidelnikov sequences of length pm – 1 is

A Note on Low Correlation Zone Signal Sets

(\frac{p+1}{2})^{m} -1

Frequency/Time hopping sequences with large linear complexities

, which is much less than its (zero-error) linear complexity.

Locally Repairable Fractional Repetition Codes

In this note, we present a connection between designing low correlation zone (LCZ) sequences and the results of correlation of sequences with subfield decompositions presented in a recent book by the first two authors. This results in low correlation zone signal sets with huge sizes over three different alphabetic sets: finite field of size q, integer residue ring modulo q, and the subset in the complex field which consists of powers of a primitive q-th root of unity. We also provide two open problems along this direction.

High Security Frequency/Time Hopping Sequence Generators

In this paper, we discuss some methods of constructing frequency/time hopping (FH/TH) sequences over GF(pk) by taking successive k-tuples of given sequences over GF(p). We are able to characterize those p-ary sequences whose k-tuple versions now over GF(pk) have the maximum possible linear complexities (LCs). Next, we consider the FH/TH sequence generators composed of a combinatorial function generator and some buffers. We are able to characterize the generators whose output FH/TH sequences over GF(pk) have the maximum possible LC for the given algebraic normal form.

Two-tuple balance of non-binary sequences with ideal two-level autocorrelation

In this paper, we introduce new locally repairable codes based on a Fractional repetition codes which is one of the MBR codes. We introduce two different constructions for different system parameters and compare these codes in terms of several performance metrics. There is some tradeoffs between the locality and other performance metrics. The newly introduced codes having the good locality should pay the price such as lower capacity or more storage nodes. And the proposed codes are more reliable than other locally repairable codes and have lower repair complexity since they can be repaired without any operations.

One-error linear complexity over Fp of Sidelnikov sequences

We consider the pk -ary frequency/time hopping (FH/TH) sequence generator composed of a combinatorial function generator and k registers. We consider possible attacks on the FH/TH sequence generator and characterize the generator with desired cryptographic properties to resist these possible attacks on a case by case basis.