Let C1 and C2 be cyclic codes over , with generator polynomials g₁ (x)

Question

Let C₁ and C₂ be cyclic codes over $\mathbb{F}_{q}$ , with generator polynomials g₁ (x) and g₂(x), respectively. Prove that C₁ $\subseteq$ C₂ if and only if g₂(x) | g¹(x).

20 Feb 2025

Answer :

Word Count : 433

We are tasked with proving that if $ C_1 \subseteq C_2 $, then the generator polynomial $ g_2(x) $ divides $ g_1(x) $, and vice versa, that is, if $ g_2(x) $ divides $ g_1(x) $, then $ C_1 \subseteq C_2 $. ### Definitions: 1. Cyclic Codes: A cyclic code is a type of linear block code where if a codeword is part of the code, then any cyclic shift of that ______ __________ ___ __________ _________ ______ ________ ______ _________ ___ ___ ___.
_____ _______ ___ _____ __________.
___ ___ ____ ________ __________ ___ _________.
_____ _______ ___ ______ _________ ______ _______ _______ _____ __________ ______.
_____ __________ ____ ________ ______ _________ __________ ___ __________ ___.
____ ___ __________ _________ _________ _____ __________ _______ _______ ________ _________.
____ _________ ___ ____ ________ ______.
_________ __________ _____ ________ _______ _____ _______ ___ _____.
___ _________ __________ __________ ________ ___ _______.
____ ____ _____ _________ ___ ________.
___ _______ _______ _______ ____ __________ _________ __________ _________ ______ _____.
___ ________ ______ _________ ___ ________.
_________ ___ ___ _________ ________ _________ _________ _________ _________ ___ _____.
_______ ______ ___ _________ ____ _________.
_________ __________ _______ ________ _______.
____ _____ ___ _________ ___ ________ ______ _______.
_________ _________ ___ _____ ____ ________.
_____ _____ ___ _____ _____.
_____ ___ _______ __________ ________.
___ __________ _________ _______ __________ ______ __________ ___ __________ ___.
________ ______ ________ ________ ______ __________ ___ ________ _______ _________.
__________ ____ __________ _____ _____ ________ _________ __________ ________ _______ _______ ___.
_________ ___ _______ _______ ____ ________ ______ _____ _________ ______ ________ ________.
_________ ____ ___ ______ ______ ________ _________.
__________ ____ __________ ___ ___ __________ _______ ____ _______ ____ __________.
____ _________ ____ _____ __________ __________ _________ _______.
______ __________ ______ _____ _____ ____ ____ _________ ______.
__________ ________ __________ ___ _____ _____ _______ ________ _________ ________ ___.
_______ ____ ___ ________ _________ ________ ___ _________ ________ _____ ______ ___.
___ _____ ___ ___ _____ _________ _________ __________ ____.
__________ _________ ___ ______ ___ ___ ________ _________ _____.
______ _______ _________ _____ ______ _________ ___ ____ ________ __________.
___ ________ _________ ___ ___ ___ _____ ______ ______ ____ _____ ______.
___ __________ ___ _________ ______ ____.
_____ ________ ____ __________ __________ ____.
___ ________ __________ ______ _________ ____ ___ _____ _________ ______ ________ ________.
________ _______ _____ __________ ___ ___ ___ ________ ___.
_____ _______ __________ _______ _____ __________ _______ ____.
_________ ______ ______ _____ _____ ________ _________.
______ ___ _______ _________ _____ _____ ____ __________ ______ __________ ___.
___ ______ _______ _____ _____.
___ _________ __________ ____ __________ ____ ___.
_________.
Get Full Answer on WhatsApp

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers

IGNOU NEWS

Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★