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2020•International Journal For Innovative Engineering and Management ResearchOpen access

THE AUNU GENERATED [ 7 4 ]-LINEAR CODE AND THE KNOWN [7 4 3 ] HAMMING CODE USING THE (U|U+V)

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Abstract

In this communication, we enumerate the construction of a [7 4 2]- linear code which is an extended code of the [ 6 4 1 ] code and is in one-one correspondence with the known [ 7 4 3 ] - Hamming code. Our construction is due to the Carley table for n=7of the generated points of was permutations of the (132) and (123)-avoiding patterns of the non-associative AUNU schemes. Next, [ 7 4 2 ] linear code so constructed is combined with the known Hamming [ 7 4 3 ] code using the ( u|u+v)-construction to obtain a new hybrid and more practical single [14 8 3 ] error- correcting code.

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In this communication, we enumerate the construction of a [7 4 2]- linear code which is an extended code of the [ 6 4 1 ] code and is in one-one correspondence with the known [ 7 4 3 ] - Hamming code. Our construction is due to the Carley table for n=7of the generated points of was permutations of the (132) and (123)-avoiding patterns of the non-associative AUNU schemes. Next, [ 7 4 2 ] linear code so constructed is combined with the known Hamming [ 7 4 3 ] code using the ( u|u+v)-construction to obtain a new hybrid and more practical single [14 8 3 ] error- correcting code.

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Available abstract

In this communication, we enumerate the construction of a [7 4 2]- linear code which is an extended code of the [ 6 4 1 ] code and is in one-one correspondence with the known [ 7 4 3 ] - Hamming code. Our construction is due to the Carley table for n=7of the generated points of was permutations of the (132) and (123)-avoiding patterns of the non-associative AUNU schemes. Next, [ 7 4 2 ] linear code so constructed is combined with the known Hamming [ 7 4 3 ] code using the ( u|u+v)-construction to obtain a new hybrid and more practical single [14 8 3 ] error- correcting code.

Key concepts: Hamming code, Constant-weight code, Code (set theory), Cyclic code, Dual code, Polynomial code, Linear code, Hamming bound

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THE AUNU GENERATED [ 7 4 ]-LINEAR CODE AND THE KNOWN [7 4 3 ] HAMMING CODE USING THE (U|U+V) — Research Paper | ScholarLens