On the Non-Existence of Certain Classes of Perfect $p$ -Ary Sequences and Perfect Almost $p$ -Ary Sequences

Abstract

We obtain new non-existence results of perfect $p$ -ary sequences with period $n$ (called type $[p, n]$ ). The first case contains a class with type $[p\equiv 5\pmod 8,p^{a}qn']$ . The second case contains five types $[p\equiv 3\pmod 4,p^{a}q^{l}n']$ for certain $p, q$ , and $l$ . Moreover, we also obtain similar non-existence results of perfect almost $p$ -ary sequences.