Development of symmetric cryptosystem using matrices with less overhead on communication channel

Many systems have been developed by mathematicians using symmetric and Asymmetric Cryptography e.g. Ceaser Cipher, Stream Ciphers, RSA, DES, IDEA, RC-4, ElGamal signatures, LFSR, Ext. Euclidean Algorithm, Lamport Signatures, Merkle Hellman Knapsack. Etc [1]. Some of them are very strong to be broken by cryptanalysts. Some are very easy and even can be broken by the measuring the frequency of alphabets in a specific cipher text. All these system carries some overhead of key with which a plain text is encrypted, for the communication channel. I thought of an idea in which product component which will be 5*1 matrix will be carried on the communication channel rather than 5*5. This 5*5 will be obtained on the receiver side inversing and producting the received matrix with symmetric key which will be known to both sender and receiver. This idea is achieved by peeping into the systems of CDMA (Code Division Multiple Access) [6] in which Walsh tables are minimized by multiplying and less overhead is achieved by communication channel. I am applying that idea in the context of cryptosystems. My Cryptosystem is that much strong enough to be broken by cryptanalyst but fewer loads for communication channel especially for Wireless Networks, Ad-Hoc Networks and Sensor Networks in minimum energy and less memory usage is main goal. The name suggested for this cryptosystem is as BasitMaxCryptoSystem.