On the Non-existence of certain classes of perfect p-ary sequences and perfect almost p-ary sequences

TL;DR

This paper establishes new non-existence results for certain classes of perfect p-ary and almost p-ary sequences, advancing understanding of their mathematical limitations based on specific modular and algebraic conditions.

Contribution

The paper introduces novel non-existence theorems for perfect p-ary sequences with particular period types, expanding the theoretical framework in sequence design.

Findings

Proves non-existence of perfect p-ary sequences for type [p ≡ 5 mod 8, p^a q n']

Establishes non-existence for five types [p ≡ 3 mod 4, p^a q^l n'] under certain conditions

Derives similar non-existence results for 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 is a class with type [p\equiv5\pmod 8,p^aqn']. The second case contains five types [p\equiv3\pmod 4,p^aq^ln'] for certain $p, q$ and $l$. Moreover, we also have similar non-existence results for perfect almost p-ary sequences.