<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2016-10-28</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000202058</issuerCik>
        <issuerName>HARRIS CORP /DE/</issuerName>
        <issuerTradingSymbol>HRS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001246989</rptOwnerCik>
            <rptOwnerName>FRADIN ROGER</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>HONEYWELL INTERNATIONAL INC.</rptOwnerStreet1>
            <rptOwnerStreet2>115 TABOR ROAD</rptOwnerStreet2>
            <rptOwnerCity>MORRIS PLAINS</rptOwnerCity>
            <rptOwnerState>NJ</rptOwnerState>
            <rptOwnerZipCode>07950</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>No Securities Beneficially Owned</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes></footnotes>

    <remarks>Exhibit List:

Exhibit 24 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>By:  /s/ Scott T. Mikuen, Attorney-in-Fact,
For:  Roger B. Fradin</signatureName>
        <signatureDate>2016-10-31</signatureDate>
    </ownerSignature>
</ownershipDocument>
