The $ b $-weight distribution for MDS codes
نویسندگان
چکیده
For a positive integer $ b\ge2 $, the b $-symbol code is new coding framework proposed to combat $-errors in read channels. Especially, 2 called symbol-pair code. Remarkably, classical maximum distance separable (MDS) also an MDS Recently, for any \mathcal{C} Ma and Luo determined weight distribution of $. In this paper, by calculating number solutions some equations utilizing shortened codes we give connection between $-weight codewords with special shape. Note that are codes, these shape shorten method r $-combinations multiset problem. From above calculation, determined. Our result generalizes corresponding [15].
منابع مشابه
Dynamic Group Key Distribution Using MDS Codes
Efficient key distribution is an important problem for secure group communications. In this paper, we present a new group key distribution scheme that supports dynamic multicast group membership changes. Instead of using encryption algorithms, the scheme employs MDS codes, a class of error control codes. The scheme achieves both forward and backward secrecy of sessions using freshly generated r...
متن کاملOn a one-parameter family of Riordan arrays and the weight distribution of MDS codes
We use the formalism of the Riordan group to study a one-parameter family of lower-triangular matrices related to the weight distribution of maximum distance separable codes. We obtain factorization results for these matrices. We then derive alternative expressions for the weight distribution of MDS codes. We define related weight ratios and show that they satisfy a certain linear recurrence.
متن کاملThe Partition Weight Enumerator and Bounds on Mds Codes
Maximum Distance Separable (MDS) codes are those error correction codes that meet the singleton bound, thus they have the largest minimum distance possible. The main research problem is to find an upper bound on the length of the codewords when the alphabet size and dimension of the code are fixed. This paper will present a new technique using the Partition Weight Enumerator for solving this pr...
متن کاملOn the weight distribution of convolutional codes
Detailed information about the weight distribution of a convolutional code is given by the adjacency matrix of the state diagram associated with a controller canonical form of the code. We will show that this matrix is an invariant of the code. Moreover, it will be proven that codes with the same adjacency matrix have the same dimension and the same Forney indices and finally that for one-dimen...
متن کاملExtending MDS Codes
A q-ary (n,k)-MDS code, linear or not, satisfies n≤ q+ k−1. A code meeting this bound is said to have maximum length. Using purely combinatorial methods we show that an MDS code with n = q + k− 2 can be uniquely extended to a full length code if and only if q is even. This result is best possible in the sense that there is, for example, a non-extendable 4-ary (5,4)-MDS code. It may be that the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics of Communications
سال: 2023
ISSN: ['1930-5346', '1930-5338']
DOI: https://doi.org/10.3934/amc.2023028