Almost Affine Codes

An almost affine code is a code C for which the size of all codes obtained by multiple puncturing of C is a power of the alphabet size. Essentially, almost affine codes are the same as ideal perfect secret haring schemes or partial affine geometries. The present paper explores these interrelations, gives short proofs of known and new results, and derives some properties of the distance distribution of almost affine codes.

[1]  Keith M. Martin,et al.  Geometric secret sharing schemes and their duals , 1994, Des. Codes Cryptogr..

[2]  G. R. Blakley,et al.  Linear Algebra Approach to Secret Sharing Schemes , 1993, Error Control, Cryptology, and Speech Compression.

[3]  Paul D. Seymour.  On secret-sharing matroids , 1992, J. Comb. Theory, Ser. B.

[4]  Ludovicus Marinus Gerardus Maria Tolhuizen,et al.  On maximum distance separable codes over alphabets of arbitrary size , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[5]  J. Simonis.  MacWilliams identities and coordinate partitions , 1995 .

[6]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[7]  Richard M. Wilson,et al.  A course in combinatorics , 1992 .

[8]  Gustavus J. Simmons,et al.  How to (Really) Share a Secret , 1988, CRYPTO.

[9]  Amos Beimel,et al.  Universally ideal secret-sharing schemes , 1994, IEEE Trans. Inf. Theory.

[10]  Marten van Dijk.  A Linear Construction of Perfect Secret Sharing Schemes , 1994, EUROCRYPT.